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Mental Math Worksheets Hub Page

Welcome to our Mental Math worksheets for developing quick and accurate mental arithmetic skills.

On this page are links to our collection of worksheets which will help your child improve their mental calculation and problem solving skills and learn their Math facts.

We also have links to our Math fact resources and online practice zones to help develop mental arithmetic.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Mental Math Worksheets

The best way to improve your mental arithmetic is to practise regularly. Even 5 minutes daily practise can make a huge difference in a matter of weeks.

Below you will find links to many different webpages containing mental math worksheets as well as mental arithmetic sheets for each of the 4 operations: addition, subtraction, multiplication and division.

There are also some links to printable math games which you can print and play at home, and watch as your child progresses.

Mental Math Tests / Quizzes

Here you will find a range of printable mental math quizzes to help your child revise their math facts and problem solving skills.

The tests/quizzes are perfect for general practice, or for keeping skills sharp.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• First Grade Mental Math
• Mental Math Worksheets 2nd Grade
• Mental Math 3rd Grade
• Mental Math Worksheets 4th Grade
• Mental Math 5th Grade
• Mental Math Worksheets 6th Grade

UK Mental Maths Worksheets

Here you will find a range of printable mental math worksheets for children in the UK to enjoy.

The language and maths skills have been adapted to support learning for primary age children.

• Mental Maths Worksheets UK

Mental Arithmetic Resources

Here you will find our selection of free resources such as flashcards and 100 squares to help your child to count and learn their addition facts.

• Math Fact Resources

Here you will find a selection of number bond sheets designed to help your child improve their recall of their number bond facts.

Online Number Bonds Practice

In our Number Bonds Practice area, you can practice your number bonds to a variety of numbers. Test your numbers bonds to 10, 20 , 100 or even 1000. Want to try decimals - you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Number Bonds Practice Zone

Number Bond Sheets

• Number Bonds to 10 and 12
• Number Bonds to 20
• Number Bonds to 50 and 100

Addition Mental Math Sheets

Here you will find a selection of mental math worksheets designed to help your child improve their recall of Addition Facts.

• Addition Practice Zone

Here is our online learning math addition zone, where you can practice a range of integer addition calculations.

Test yourself on the following addition facts:

• up to 5+5, 10+10, 20+20, 50+50, 100+100, or 1000+1000;
• 2 digit numbers adding ones;
• 2 digit numbers adding tens;
• 3 digit numbers adding hundreds;

Addition Worksheet Generator

Here is our free generator for addition worksheets.

This easy-to-use generator will create randomly generated addition worksheets for you to use.

Each sheet comes complete with answers if required.

The areas the generator covers includes:

• addition with numbers up to 10, 15, 20, 50, 100 and 1000;
• addition by 10s with 2 digit numbers;
• addiiton by 100s with 3 digit numbers;
• addition with numbers to 10 with one decimal place;
• addition with numbers to 1 with 2 decimal places.

These generated sheets can be used in a number of ways to help your child with their addition fact learning.

• Free Addition Worksheets (randomly generated)

Adding to 10 Sheets

Here you will find a selection of mental math worksheets designed to help your child improve their adding up to a total of 10.

Using these sheets will help your child learn to:

• add numbers up to a total of 10.
• Addition Math Worksheets to 10

Adding to 12+12

Here you will find a range of mental math worksheets designed to help you child to learn their Addition facts to 12+12.

• Addition Fact Practice to 12
• Addition Facts to 20 Worksheets
• First Grade Addition and Subtraction to 12

Addition to 20+20

Here you will find a range of Addition Sheets designed to help you child to learn their Addition facts to 20+20.

• Math Addition Facts to 20

Addition to 100+100

The following mental math worksheets develop children's knowledge of practicing their Addition facts up to 100+100.

• Third Grade Addition Facts Worksheets to 100+100

Decimal Addition Facts

The following sheets develop children's understanding of place value and decimals as well as applying their addition fact knowledge of to work out their decimal addition facts.

• Decimal Math Worksheets

Subtraction Fact Sheets

Here you will find a selection of Mental Subtraction sheets designed to help your child improve their recall of Subtraction Facts.

Online Subtraction Practice Zone

Here is our online learning math subtraction practice area where you can test yourself on your subtracting skills.

Test yourself on the following integer subtraction facts:

• up to 10, 15, 20, 50, 100, 200, 500 or 1000;
• 2 digit subtract ones;
• 2 digit subtract tens;
• 3 digit subtract hundreds.
• Subtraction Practice Zone

Subtraction Worksheet Generator

Here is our free generator for subtraction worksheets.

This easy-to-use generator will create randomly generated subtraction worksheets for you to use.

• subtraction with numbers up to 10, 15, 20, 50, 100 and 1000;
• subtraction by 10s from 2 digit numbers;
• subtraction by 100s from 3 digit numbers;
• subtraction with numbers to 10 with one decimal place;
• subtraction with numbers to 1 with 2 decimal places;
• subtraction involving negative numbers.
• Free Subtraction Worksheets (randomly generated)

Subtracting to 10 Sheets

Here you will find a selection of Subtraction sheets designed to help your child learn their Subtraction facts up to 10.

• Kindergarten Subtraction Worksheets (easier)
• Subtraction to 10 Worksheets (harder)
• Subtraction Facts to 12

Here you will find a range of Free Printable First Grade Subtraction Sheets designed to help you child to learn their Subtraction facts to 12.

Subtraction Facts to 20

Here you will find a range of Free Printable 2nd Grade Subtraction Sheets designed to help you child to learn their Subtraction facts to 20.

• Subtraction Facts to 20 Worksheets

Subtraction Facts to 100

The following sheets develop children's knowledge of their Subtraction facts up to 100.

• Third Grade Subtraction Worksheets to 100

Decimal Subtraction Facts

The following sheets develop children's understanding of place value and decimals as well as applying their Subtraction fact knowledge to work out their decimal Subtraction facts.

• Subtracting Decimals Worksheets (mental)

Multiplication Times Tables Sheets

Here you will find a selection of Mental Multiplication sheets designed to help your child improve their mental recall of Multiplication Facts and learn their times tables.

Online Multiplication Test

Here is our online learning math practice zone for multiplication facts.

Using this zone is a great way to test yourself on your facts and see how many you can do in a minute.

Then re-test yourself and see if you can improve your score.

Using this zone, you can:

• choose tables up to 5x5, 10x10 or 12x12 to test yourself on;
• select one or more tables to test yourself on;
• practice multiplying whole numbers by 10 or 100.
• Online Multiplication Zone

Multiplication Worksheet Generator

Here is our free generator for multiplication worksheets.

This easy-to-use generator will create randomly generated multiplication worksheets for you to use.

• Multiplying with numbers to 5x5;
• Multiplying with numbers to 10x10;
• Multiplying with numbers to 12x12;
• Practicing a single times table;
• Practicing selected times tables;

These generated sheets can be used in a number of ways to help your child with their times table learning.

• Times Tables Worksheets (randomly generated)

Tiimes Table Graded Sheets

As your child progresses through the grades, they will learn their multiplication table to 5x5 and eventually to 10x10, or 12x12.

Once they know their multiplication facts, they can start to learn related facts, e.g. if 3 x 4 = 12, then 30 x 4 = 120 and $300 x 4 = $1200.

• Math Times Table Worksheets

Multiplication by 10s and 100s

These Multiplication Printable Worksheets below are designed to help your child improve their ability to multiply a range of numbers by multiples of 10 and 100 mentally.

• Multiplying by Multiples of 10 and 100

Mental Multiplication Decimals

These Multiplication Printable Worksheets below involve children using their multiplication table facts to answer related questions involving decimals.

• Multiplying Decimals by Whole Numbers

Division Fact Sheets

Here you will find a selection of Mental Division sheets designed to help your child improve their recall of Division Facts and to apply their facts to answer related questions.

Online Division Practice Area

Here is our free division practice area.

If you want to practice your division facts, or take a timed division test, then this is the place for you.

In this area, we cover the following division facts:

• division facts up to 5x5, up to 10x10 or up to 12x12;
• division facts linked to individual tables facts;
• dividing by 10 and 100.
• Division Practice Zone

Division Worksheet Generator

Here is our free generator for division worksheets.

This easy-to-use generator will create randomly generated division worksheets for you to use.

• Dividing with numbers to 5x5;
• Dividing with numbers to 10x10;
• Dividing with numbers to 12x12;
• Dividing with a single times table;
• Practicing division with selected times tables;

These generated sheets can be used in a number of ways to help your child with their division table learning.

• Division Facts Worksheets (randomly generated)

Division Facts to 10x10 Sheets

Here you will find a selection of Division sheets designed to help your child learn their Division facts up to 10x10.

Example: if a child knows that 5 x 4 = 20, then they should also know that 20 ÷ 5 = 4 and 20 ÷ 4 = 5.

• Division Facts to 10x10 Worksheets

Division Related Facts 10s and 100s

Here you will find a selection of Division sheets designed to help your child learn to use their Division facts up to 10x10 to answer related questions.

Example: if you know that 42 ÷ 6 = 7, then you also know that 420 ÷ 6 = 70 or 420 ÷ 70 = 6, etc.

• Divding by Multiples of 10 and 100 Worksheets

Math Fact Games

Here you will find a range of Free Printable Math Fact Games.

The following games develop a range of mental Math skills in a fun and motivating way.

Using these sheets will help your child to:

• learn their Math facts;
• develop their strategic thinking skills.
• Math Addition Games
• Subtraction Games
• Multiplication Math Games
• Math Division Games

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Mental Math Practice

This is a page where you can practice your mental math skills to your heart's desire (for free!)

What problems should I select to solve?

When engaging with our tool, you're encouraged to tackle math problems that you find most challenging or want to improve upon. Whether it's basic operations like addition and subtraction, or more complex calculations involving multiplication and division, the choice is yours. Tailoring your practice to areas where you feel less confident not only enhances your skills but also builds confidence in your abilities. Explore a variety of arithmetic problems to discover which ones you'd like to master or need more help with.

Why is mental math considered an essential skill to develop?

Math is more than just a school subject; it's a critical life skill that aids in daily decision-making and problem-solving. Whether you're calculating change, comparing prices, budgeting for expenses, or estimating time, the ability to quickly perform calculations in your head is invaluable. In the business world, mental arithmetic can help you analyze data, manage finances, and make strategic decisions swiftly. By improving your mental math skills, you're not just learning numbers; you're enhancing your ability to think critically and make informed decisions in everyday life and professional settings.

How often should I practice to improve my skills?

The amount of math practice needed to enhance your arithmetic skills varies depending on your goals and current proficiency. The key is consistent practicing and striving for continuous improvement. Whether you engage in mental math practices daily or at a pace that fits your schedule, it's essential to keep challenging yourself and to recognize progress, no matter how small. If you find yourself hitting a plateau or seeking more structured guidance, our lessons page offers additional resources and drills to further develop your skills. Remember, the journey to improvement is personal, and continuing to see progress is what truly matters!

Is there a fact or principle that makes math practice easier?

Indeed, math practice becomes more manageable when you understand the underlying principles and strategies that simplify calculations. Our lessons page is a treasure trove of such techniques, designed to strengthen your number sense and enhance your ability to solve math exercises more efficiently. From reinforcing basic facts to developing shortcuts for complex calculations, these principles (and each subsequent drill) are fundamental to becoming proficient. By familiarizing yourself with these strategies through our lessons, you'll find that approaching and solving mental math exercises becomes easier and more intuitive.

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Mental Math Strategies for Addition Worksheet FREEBIE L1 2nd Grade iReady Math

• Easel Activity

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Description

Teach 2nd-grade students how to use mental math strategies for addition with these math worksheets, exit tickets, and vocabulary activities. Whether you teach iReady Math or another curriculum, these print and digital problems align with Common Core State Standards and prepare students for standardized testing. Assign the lesson checks about adding using mental math as homework or share them in small groups. Present these rigorous math questions in PowerPoint or Google Classroom through TPT Easel. 

Check out the Contents of Lesson 1 - Mental Math Strategies for Addition:

✏️ Two Vocabulary Worksheets that align with terms in the lesson

• Students will strengthen their understanding of this lesson’s vocabulary terms through fun activities.

✏️ Two Levels of Practice Pages (4 worksheets)

• Basic (On Level) - Provide additional practice with grade-level math.
• Advanced (Challenge) - Plunge deeper into grade-level math and apply knowledge.
• These “Lesson Checks” can be used for reteaching, independent work, assessment, math centers, or math homework.

✏️ Two Exit Tickets for Every Session (Printed two/page; most lessons have 5 sessions)

✏️ PowerPoint File

• All questions have been reformatted for screens 
• Add interactive elements with PearDeck or Nearpod.
• Export the slides to OneNote, Google, or SeeSaw!

✏️ Answer Keys

Use These Worksheets and Exit Tickets with your iReady Classroom Math Curriculum!

✅ Differentiate by assigning “Basic” (>) worksheets to students who are practicing grade-level content. Challenge gifted and talented students with “Advanced” (>>) worksheets. These activities require students to dive deeper as they use mental math strategies for addition.

✅ Complete one lesson check in small groups and assign a second page for homework. (Questions prepare students to master iReady Classroom Math Quizzes!)

✅ Invite early finishers to think creatively about math vocabulary through a variety of activities.

✅ Quickly assess students’ math abilities with the exit tickets. 

Hear From Educators Like You!

⭐️ “You will not regret purchasing this product. They are great resources and very well planned out. I love the exit tickets.”

⭐️ “I am in love with these resources! I use the exit tickets every day and I also use the worksheets as homework and assessments.”

⭐️ “Since iReady is new to me, I needed a guide to help me with exit tickets, homework, and extra practice for my students. This does just that. It has been so useful and I am so excited to keep using this resource.”

Find Answers about this Supplement to your 2nd Grade Math Curriculum:

✋ Does my district have to use iReady Classroom Math 2020?

• No, these worksheets and exit tickets align with CCSS and provide excellent practice to students in all math classes. Don’t take my word for it… teachers like you have said, “This was awesome! I LOVE the range of problem types! My school doesn’t use iReady and I still LOVED these slides!”

✋ I use PearDeck...Google Classroom...SeeSaw... Will the digital elements work?

• Yes! Every question has been reformatted to make digital integration a breeze! Present with PearDeck, NearPod, or PowerPoint. Export the slides into SeeSaw or OneNote. It’s so easy!

Did you know? You can assign TPT Easel resources, like like this lesson on how to use mental math strategies for addition, to Google Classroom! If you don’t teach in a “Google” school, share TPT Easel with students through a link. Save time and paper by assigning online!

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Welcome to the Math Medic Precalculus course! The lessons and activities in this course are designed to thoughtfully prepare students for AP Calculus or other college math courses. Each lesson is designed to be taught in an Experience First, Formalize Later (EFFL) approach, in which students work in small groups on an engaging activity before the teacher formalizes the learning. Alignment to the CCSS can be found here .

The course begins with an in-depth study of function families, with a focus on connecting multiple representations, followed by an advanced investigation of trigonometry and its applications, including polar graphs, parametric equations, and vectors. The course continues with a unit on sequences and series followed by an accessible and engaging introduction to the big ideas of Calculus. The unit overviews and learning targets for the Math Medic Precalculus course can be found here .

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Homework Practice 2 1 Mental Math

Homework Practice 2 1 Mental Math - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Homework practice and problem solving practice workbook, Mental math, Sample work from, 2 the property, Grade 2 addition work, Reteach workbook grade 2 pe, Chapter 4 adding and subtracting using mental math, Math mammoth grade 2 a light blue complete curriculum.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Homework Practice and Problem-Solving Practice Workbook

2. mental math, 3. sample worksheet from www.mathmammoth, 4. 2 the property, 5. grade 2 addition worksheet, 6. reteach workbook, grade 2 (pe) -, 7. chapter 4 adding and subtracting using mental math, 8. math mammoth grade 2-a light blue complete curriculum.

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Big Ideas Math Answers Grade 3 Chapter 8 Add and Subtract Multi-Digit Numbers

Hey Guys!!! Are you looking for solutions for BIM Grade 3 Chapters? If your answer is yes, then you are on the right page. Here the students can get a clear cut explanation for all the Big Ideas Math Answers Chapter 8 Add and Subtract Multi-Digit Numbers. It is necessary for you to learn the basics from the primary level itself. The Big Ideas Math Book 3rd Grade Answer Key Chapter 8 Add and Subtract Multi-Digit Numbers helps you overcome the issues you face while solving the problems.

Big Ideas Math Book 3rd Grade Answer Key Chapter 8 Add and Subtract Multi-Digit Numbers

First, go through the topics covered in this chapter to know which topic is easy and which is difficult. Practice the questions a number of times to understand the concepts in depth. To make your task easy we have provided the links in the below section. Just hit the links and Download Big Ideas Math Answers Grade 3 Chapter 8 Add and Subtract Multi-Digit Numbers pdf.

Lesson 1 – Identify Addition Properties

Lesson 8.1 Identify Addition Properties

Identify addition properties homework & practice 8.1.

Lesson 2 – Use Number Lines to Addition

Lesson 8.2 Use Number Lines to Addition

Use number lines to addition homework & practice 8.2.

Lesson 3 –  Use Mental Math to Add

Lesson 8.3 Use Mental Math to Add

Use mental math to add homework & practice 8.3.

Lesson 4 – Use Partial Sums to Add

Lesson 8.4 Use Partial Sums to Add

Use partial sums to add homework & practice 8.4.

Lesson 5 – Add Three-Digit Numbers

Lesson 8.5 Add Three-Digit Numbers

Add three-digit numbers homework & practice 8.5.

Lesson 6 – Add Three or More Numbers

Lesson 8.6 Add Three or More Numbers

Add three or more numbers homework & practice 8.6.

Lesson 7 – Use Number Lines to Subtract

Lesson 8.7 Use Number Lines to Subtract

Use number lines to subtract homework & practice 8.7.

Lesson 8 – Use Mental Math to Subtract

Lesson 8.8 Use Mental Math to Subtract

Use mental math to subtract homework & practice 8.8.

Lesson 9 – Subtract Three-Digit Numbers

Lesson 8.9 Subtract Three-Digit Numbers

Subtract three-digit numbers homework & practice 8.9.

Lesson 10 – Relate Addition and Subtraction

Lesson 8.10 Relate Addition and Subtraction

Relate addition and subtraction homework & practice 8.10.

Lesson 11 – Problem Solving: Addition and Subtraction

Lesson 8.11 Problem Solving: Addition and Subtraction

Problem solving: addition and subtraction homework & practice 8.11.

Performance Task

Add and Subtract Multi-Digit Numbers Performance Task

Add and subtract multi-digit numbers activity, add and subtract multi-digit numbers chapter practice, add and subtract multi-digit numbers cumulative practice 1 – 8, add and subtract multi-digit numbers steam performance task 1-8.

Explore and Grow

Structure Use the addition table to write all of the equations that have a sum of 12. What do you notice?

Answer: Add blue line and yellow line. Add 10 in the blue column and 2 in the yellow column. 10 + 2 = 12 Thus the addition equation has the sum of 12.

Think and Grow: Addition Properties Changing the order of addends does not change the sum. 3 + 5 = 5 + 3 Associative Property of Addition Changing the grouping of addends does not change the sum. (7 + 6) + 4 = 7 + (6 + 4) Addition Property of Zero The sum of any number and 0 is that number. 9 + 0 = 9 Example Identify the property. 56 + 0 = ___ 12 + 29 = 29 + 12 _____ (24 + 17) + 23 = 24 + (17 + 23) ____

Answer: 56 + 0 = 56 It shows Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number. 12 + 29 = 29 + 12 Changing the order of addends does not change the sum. (24 + 17) + 23 = 24 + (17 + 23) It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Show and Grow

Identify the property.

Question 1. 16 + (14 + 19) = (16 + 14) + 19

Answer: It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 2. 11 + 54 = 54 + 11

Answer: Associative Property of Addition defines the changing the order of addends does not change the sum.

Question 3. 0 + 43 = 43

Answer: Addition Property of Zero The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 4. (27 + 18) + 22 = 27 + (18 + 22)

Apply and Grow: Practice

Question 5. (28 + 16) + 14 = 28 + (16 + 14)

Question 6. 12 + 35 = 35 + 12

Question 7. 36 + 0 = 36

Answer: The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 8. 11 + (9 + 57) = (11 + 9) + 57

Find the missing number.

Question 9. 23 + 45 = 45 + ___

Explanation: Let the missing number be x. By using the Associative Property of Addition property we can find the missing number. 23 + 45 = 45 + x 23 + 45 = 45 + 23 Thus the missing number is 23.

Question 10. (13 + 12) + __ = 13 + (12 + 45)

Explanation: Let the missing number be x. By using the Associative Property of Addition property we can find the missing number. (13 + 12) + x = 13 + (12 + 45) Thus the missing number is 45.

Question 11. 4 + (76 + 10) = (___ + 76) + 10

Explanation: Let the missing number be x. By using the Associative Property of Addition property we can find the missing number. 4 + (76 + 10) = (x + 76) + 10 4 + (76 + 10) = (4 + 76) + 10 Thus the missing number is 4.

Question 12. 98 + ___ = 98

Explanation: Let the missing number be x. The Addition Property of Zero defines the sum of any number and 0 is that number. 98 + x = 98 x = 98 – 98 x = 0 Thus the missing number is 0.

Question 13. (___ + 0) + 32 = 6 + 32

Explanation: Let the missing number be x. By using the Associative Property of Addition property we can find the missing number. (x + 0) + 32 = 6 + 32 x + 32 = 38 x = 38 – 32 x = 6 Thus the missing number is 6.

Question 14. 64 + (5 + 23) = (23 + ___) + 64

Explanation: Let the missing number be x. By using the Associative Property of Addition property we can find the missing number. 64 + (5 + 23) = (23 + x) + 64 64 + 28 = 23 + x + 64 82 = x + 87 x = 87 – 82 x = 5 Thus the missing number is 5.

Question 15. DIG DEEPER! Use the numbers 24, 54, and 11 to write an equation that shows the Associative Property of Addition.

Answer: We can write the equation by using the Associative Property of Addition. 24 + (54 + 11) = (24 + 54) + 11

Writing Use a property to find the sum. Which property did you use? Why?

Question 16. 54 + 0 = __

Explanation: We can find the sum of the 54 + 0 by using the addition property of zero. The Addition Property of Zero defines the sum of any number and 0 is that number. 54 + 0 = 54

Question 17. (46 + 17) + 33 = ___

Explanation: We can find the sum of the (46 + 17) + 33 by using the Associative Property of Addition. (46 + 17) + 33 = 96

Question 8. 20 + 63 = ___

Explanation: We can find the sum of the Associative Property of Addition. 20 + 63 = 83

Think and Grow: Modeling Real Life

Answer: Given, A tourist visits 13 museums, 19 memorials, and 11 monuments. We can find the total number of sites the tourist visits. (13 + 19) + 11 = 13 + (19 + 11) = 43 Thus the tourist visits 43 sites.

Question 19. A farmer sells 34 cucumbers, 48 ears of corn, and 26 bell peppers at a farmer’s market. Explain how to use properties to find the total number of vegetables the farmer sells. (34 + 48) + 26 = ?

Answer: Given, A farmer sells 34 cucumbers, 48 ears of corn, and 26 bell peppers at a farmer’s market. We can find the sum of the Associative Property of Addition. (34 + 48) + 26 = 34 + (48 + 26) 34 + 48 + 26 = 108 Thus the total number of vegetables the farmer sells is 108.

Answer: The number of adults = 20 The number of grade 2 students = 47 The number of grade 3 students = 53 20 + 47 + 53 = 120 Thus 120 people go on the field trip.

DIG DEEPER! The Grade 2 and Grade 3 students are divided into 10 equal groups. How many students are in each group? Explain.

Answer: Given that, The Grade 2 and Grade 3 students are divided into 10 equal groups. The number of grade 2 students = 47 The number of grade 3 students = 53 47 + 53 = 100 100/10 = 10 Thus there are 10 students in each group.

Question 1. (79 + 12) + 13 = 79 + (12 + 13)

Answer: Associative property of addition It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 2. 24 + 63 = 63 + 24

Question 3. 0 + 64 = 64

Answer: Associative property of zero The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 4. 37 + (43 + 19) = (37 + 43) + 19

Question 5. 17 + 38 = 38 + 17

Question 6. 18 + 48 = 48 + 18

Question 7. 36 + __ = 36

Explanation: Let the missing number be x. 36 + x = 36 x = 36 – 36 x = 0 Thus the missing number is 0.

Question 8. 25 + __ + 11 = 25 + 11

Explanation: Let the missing number be y. 25 + y + 11 = 25 + 11 y + 36 = 36 y = 36 – 36 y = 0 Thus the missing number is 0.

Question 9. 0 + 43 = __ + 0

Explanation: Let the missing number be t. 0 + 43 = t + 0 43 = t Thus the missing number is 43.

Question 10. (22 + 19) + 28 = 19 + (___ + 28)

Explanation: Let the missing number be p. 22 + 19 + 28 = 19 + p + 28 69 = 47 + p p = 69 – 47 p = 22 Thus the missing number is 22.

Answer: Given the expression (18 + 27) + 12 = 27 + (18 + 12) By seeing the above expression we can say that Newton used Associative Property of Addition and Commutative Property of Addition.

Question 12. Open-Ended Write an equation that shows the Commutative Property of Addition.

Answer: 4 + 2 = 2 + 4 Commutative property of addition: Changing the order of addends does not change the sum.

Question 13. Structure Explain how the Associative Property of Addition and the Associative Property of Multiplication are alike and how they are different.

Answer: Associative property explains that addition and multiplication of numbers are possible regardless of how they are grouped. Example: 2 × (3 × 5) = (2 × 3) × 5 2 + (3 + 5) = (2 + 3) + 5 The method is same but the solution for both the equations are different.

Question 14. Modeling Real Life A florist uses 11 roses, 12 lilies, and 19 daisies to make bouquets. How many flowers does he use?

Answer: Given that, A florist uses 11 roses, 12 lilies, and 19 daisies to make bouquets. Add all the flowers to find the total number of flowers he used. 11 + 12 + 19 = 42 Thus he used 42 flowers.

DIG DEEPER! The florist uses 6 flowers for each bouquet. How many bouquets does he make? Explain.

Answer: Given, The florist uses 6 flowers for each bouquet. Total flowers = 42 Divide the total number of flowers by the number of flowers in each bouquet 42/6 = 7 Thus he made 7 bouquets.

Review & Refresh

Find the product.

Answer: Multiply the two numbers 0 and 3. 0 × 3 = 0

Answer: Multiply the two numbers 7 and 7. 7 × 7 = 49

Answer: Multiply the two numbers 10 and 4. 10 × 4 = 40

Answer: Multiply the two numbers 7 and 6. 7 × 6 = 42

How can finding 33 + 25 help you find 533 + 25?

Answer: We can find the sum of 533 and 25 with the help of the above problem. 33 + 25 = 58 533+ 25 = 538 Just add 5 on the left side to get the sum.

Think and Grow: Adding on a Number Line

Find the sum

Answer: Given, Humans have 24 rib bones and 182 other types of bones. 182 + 24 = 206 Thus Humans have 206 bones.

Answer: 436 + 4 + 20 + 4 440 + 20 + 4 = 464

Question 9. Structure Show two different ways to find 225 + 39 using a number line.

Question 10. A book has 216 pages. You have already read 167 pages. You read 49 more pages. Do you finish reading the book?

Answer: Given that, A book has 216 pages. You have already read 167 pages. You read 49 more pages. 167 + 49 = 216 pages 216 – 216 = 0 Thus you finish reading the book.

Answer: Given that, A puzzle has 350 pieces. You put 95 pieces together. Your friend puts 185 pieces together. 95 + 185 = 280 pages 350 – 280 = 70 pages No you and your friend do not complete the puzzle. 70 pieces are left to complete the puzzle.

Question 12. A music library has 483 songs. You listen to162 different songs one week and 171 more songs the next week. How many songs are left?

Answer: Given that, A music library has 483 songs. You listen to162 different songs one week and 171 more songs the next week. 162 + 171 = 333 songs 483 – 333 = 150 songs Thus 150 songs are left.

Answer: Your friend uses a number line to find 435 + 27. 435 + 27 = 462 Your friend is not correct.

Question 6. YOU BE THE TEACHER Your friend says she can find 64 + 691 by starting at 691 on a number line because of the Associative Property of Addition. Is your friend correct? Explain.

Answer: Given, Your cousin needs to write a 400-word essay. She writes 318 words during class. She finishes her essay by writing 94 words at home. 318 + 94 = 412 412 – 400 = 12 Yes your cousin’s essay have enough words.

Question 8. DIG DEEPER! There are 275 apartments in an apartment building. There are 203 two-bedroom apartments rented, and 56 one-bedroom not apartments rented. How many apartments are rented?

Answer: Given that, There are 275 apartments in an apartment building. There are 203 two-bedroom apartments rented, and 56 one-bedroom not apartments rented. 203 + 56 = 259 Thus 259 apartments are rented.

Find the quotient

Question 9. 18 ÷ 6 = ___

Explanation: Divide the two numbers 18 and 6. 18/6 = 3 Thus the quotient is 3.

Question 10. 32 ÷ 8 = ___

Explanation: Divide the two numbers 32 and 8. 32/4 = 4 Thus the quotient is 4.

Question 11. 72 ÷ 9 = __

Explanation: Divide the two numbers 72 and 9. 72/9 = 8 Thus the quotient is 8.

Answer: 366 + 504 = 870

Explanation: By seeing the above figure we can find the sum. First count the number of blocks There are 100 blocks in each figure There are three 100 blocks, six 10 blocks, and 6 blocks. 300 + 60 + 6 = 366 There are five 100 blocks and 4 blocks. 500 + 4 = 504 Now add both 366 + 504 = 870

Reasoning Show how to find 402 + 248.

Answer: You can find the sum of 402 and 248 by using the above arrays. Take 10 × 10 block 402 – Four 10 × 10 blocks, 2 blocks 248 – Two 10 × 10 blocks, Four 10 blocks, and eight blocks 402 + 248 = 650

Think and Grow: Mental Math Strategies for Addition

Answer: You can find the sum of 247 and 328 by using mental math strategies. 247 + 3 = 250 328 – 3 = 325 250 +325 575 Thus the sum of 247 and 328 is 575.

Answer: 119 + 163 = 119 + (1 + 100 + 60 + 2) (119 + 1) + 100 + 60 + 2 120 + 100 + 60 + 2 382

Answer: 322 – 2 = 320 158 + 2 = 160 320 +160 480 So, 322 + 158 = 480

Answer: 695 + 187 = 695 + (5 + 100 + 80 + 2) (695 + 5) + (100 + 80 + 2) 700 + 100 + 80 + 2 882 So, 695 + 187 = 882

Answer: 604 – 4 = 600 275 + 4  = 279 600 +279 879

Answer: 359 + 1 = 360 360 + 300 = 660 660 + 17 = 677 So, 359 + 318 = 677

Use mental math to find the sum.

Question 5. 436 + 248 = __

Answer: 436 + 248 = 436 + (8 + 40 + 200) 436 + (4 + 4 + 40 + 200) (436 + 4) + 4 + 40 + 200 440 + 244 684 So, 436 + 248 = 684

Question 6. 795 + 102 = ___

Answer: 102 – 2 = 100 795 + 2 = 797 797 +100 897 So, 795 + 102 = 897

Question 7. 503 + 71 = ___

Answer: 503 – 3 = 500 71 + 3 = 74 500 +74 574 So, 503 + 71 = 574

Question 8. 589 + 407 = ___

Answer: 589 + 1 = 590 407 – 1 = 406 590 +406 996

Question 9. 734 + 97 = ___

Answer: 734 – 3 = 731 97 + 3 = 100 731 +100 831

Question 10. 352 + 164 = ___

Answer: 352 – 2 = 350 164 + 2 = 166 350 +166 516

Question 11. 297 + 211 = ___

Answer: 297 + 3 = 300 211 – 3 = 208 300 +208 508

Question 12. 426 + 364 = ___

Answer: 426 + 4 = 430 364 – 4 = 360 430 +360 790

Question 13. 159 + 104 = ___

Answer: 159 + 1 = 160 104 – 1 = 103 160 +103 263

Question 14. A community shelter collects 101 shirts and 109 pairs of pants from a clothing drive. How many clothing items does the community shelter collect?

Answer: Given, A community shelter collects 101 shirts and 109 pairs of pants from a clothing drive. 101 – 1 = 100 109 + 1 = 110 100 +110 210 Thus the community shelter collect 210 clothing items.

Answer: Descartes wants to use compensation to find 238 + 127. The number near 238 is 240, 127 is 130. Thus he could use 240 and 130

Answer: Given, A company manager has $900. The cost of the laptop is $595 The cost of the mobile is $249. 595 + 5 = 600 249 – 5 = 244 600 +244 844 900 – 844 = 56 Thus the manager does not have enough money.

Question 16. A USB drive holds 600 photos. You have 279 photos on a digital camera and 337 photos on a cell phone. Can the USB drive hold all of your photos?

Answer: Given, A USB drive holds 600 photos. You have 279 photos on a digital camera and 337 photos on a cell phone. 279 + 1 = 280 337 – 1 = 336 280 +336 616 Yes the USB drive can hold all of your photos

DIG DEEPER! The president buys the two items. How much money does she have left?

Answer: A school board president has $1,000. The cost of a swing set is $648 The cost of the seesaw is $372 The cost of a Dome Climber is $498 498 +372 870 1000 – 870 = 130 Thus she has left $130.

Use compensation to find the sum.

Answer: 248 + 2 = 250 137 – 2 = 135 250 +135 385 So, 248 + 137 = 385

Answer: 401 – 1 = 400 165 + 1 = 166 400 +166 566

Make a ten and count on to find the sum

Answer: 506 + 369 = 506 + (4 + 300 + 60 + 5) (506 + 4) + 300 + 60 + 5 510 + 365 875 So, 506 + 369 = 875

Answer: 617 + 348 = 617 + (3 + 300 + 40 + 5) (617 + 3) + 300 + 40 + 5 620 + 345 965 617 + 348 = 965

Question 5. 478 + 219 = ___

Answer: 478 + 2 = 480 219 – 2 = 217 480 +217 697

Question 6. 503 + 64 = ___

Answer: 503 – 3 = 500 64 + 3 = 67 500 +67 567

Question 7. 288 + 242 = ___

Answer: 288 + 2 = 290 242 – 2 = 240 290 +240 530

Answer: 738 + 126 = 738 + (6 + 20 + 100) (738 + 2) + 4 + 20 + 100 740 + 124 864

Question 9. Writing How is compensation make a ten similar to the strategy? How is it different?

Answer: Compensation is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve. The methods are different but the solutions are the same.

Question 10. Modeling Real Life A binder holds 250 sheets of paper. You have 107 science papers and 142 math papers. Can the binder hold all of your papers?

Answer: Given, A binder holds 250 sheets of paper. You have 107 science papers and 142 math papers. 107 – 2 = 105 142 + 2 = 144 105 + 144 = 249 Yes, the binder can hold all of your papers.

DIG DEEPER! The school nurse buys the two items. How much money does she have left?

Answer: A school nurse has $450. The cost of a Stethoscope = $119 The cost of thermometer = $ 308 119 + 1 = 120 308 – 1 = 307 120 +307 427 450 – 427 = 23 She has left $23

Question 12. It costs $1 to get into each football game. Newton buys a chicken wrap for $2 and a drink for $1 each game. How much money does Newton spend in 4 games?

Answer: Given, It costs $1 to get into each football game. Newton buys a chicken wrap for $2 and a drink for $1 each game. 1 + 2 + 1 = 4 4 × $4 = $8 Thus Newton spent $8 for 4 games.

300 + 40 + 1 200 + 20 + 7 500 + 60 + 8 = 568

Reasoning How can breaking apart addends help you add three-digit numbers?

Answer: Breaking apart addends helps you add three-digit numbers easily. Mind math is possible with this breaking apart addends.

Think and Grow: Use Partials Sums to Add

Answer: 764

Use partial sums to add.

Answer: 319 = 300 + 10 + 9 234 = 200 + 30 + 4 553 = 500 + 40 + 13

Answer: 568 = 500 + 60 + 8 173 = 100 + 70 + 3 741 = 600 + 130 + 11

Answer: 424 = 400 + 20 + 4 450 = 400 + 50 + 0 874 = 800 + 70 + 4

Answer: 281 = 200 + 80 + 1 365 = 300 + 60 + 5 646 = 500 + 140 + 6

Answer: 127 = 100 + 20 + 7 609 = 600 + 0 + 9 736 = 700 + 20 + 16

Answer: 276 = 200 + 70 + 6 39 =  000 + 30 + 9 315 = 200 + 100 + 15

Answer: 759 = 700 + 50 + 9 202 = 200 + 00 + 2 961 = 900 + 50 + 11

Answer: 864 = 800 + 60 + 4 131 = 100 + 30 + 1 995 = 900 + 90 + 5

Answer: 387 = 300 + 80 + 7 94 = 000 + 90 + 4 481 = 300 + 170 + 11

Answer: 560 = 500 + 60 + 0 273 = 200 + 70 + 3 833 = 700 + 130 + 3

Question 11. 498 + 375 = ___

Answer: 498 = 400 + 90 + 8 375 = 300 + 70 + 5 873 = 700 + 160 + 13

Question 12. 209 + 158 = ___

Answer: 209 = 200 + 00 + 9 158 = 100 + 50 + 8 367 = 300 + 50 + 17

Answer: Given, A giant panda weighs 696 pounds less than a polar bear. 696 – 263 = 433 Thus the polar bear weighs 433 pounds.

Answer: Given, A herd of wildebeests has 258 fewer members than a herd of zebras has. There are 335 wildebeests in the herd. 335 – 258 = 77 Therefore there are 77 zebras in their herd.

Answer: Given, There are three candidates in an election. Candidate A receives 184 fewer votes than Candidate B. Number of votes candidate A receives = 347 347 + 184 = 631 Thus Candidate B wins the election.

Answer: Your friend score is 579 Your friend scores 161 fewer points than you. 579 + 161 = 740 Your score is 740 Your cousin scores 213 more points than your friend. 213 + 579 = 592 Your cousin’s score is the highest among all three. So, your cousin wins the game.

Use partials sums to add

Answer: We can find the sum by using the partial sum model. 479 = 400 + 70 + 9 356 = 300 + 50 + 6 835 = 700 + 120 + 15 So, 479 + 356 = 835

Answer: We can find the sum by using the partial sum model. 674 = 600 + 70 + 4 321 = 300 + 20 + 1 995 = 900 + 90 + 5

Answer: We can find the sum by using the partial sum model. 396 = 300 + 90 + 6 278 = 200 + 70 + 8 674 = 500 + 160 + 14

Question 4. 564 + 218 = ___

Answer: We can find the sum by using the partial sum model. 564 = 500 + 60 + 4 218 = 200 + 10 + 8 782 = 700 + 70 + 12

Question 5. 190 + 123 = ___

Answer: We can find the sum by using the partial sum model. 190 = 100 + 90 + 0 123 = 100 + 20 + 3  313 = 200 + 110 + 3

Answer: Your friend is incorrect. 205 = 200 + 00 + 5 124 = 100 + 20 + 4 329 = 300 + 20 + 9 The sum of 205 + 124 = 329

Answer: The addend is increased by 100. So, the next pattern is 516 +178 694

Answer: Given, There are worker bees and drone bees in a beehive. A hive has 268 fewer drones than workers. There are 351 drone bees. 351 -268 83 Therefore there are 83 worker bees.

Answer: Three athletes compete in Olympic weight lifting. Weight lifter A lifts 104 fewer pounds than Weight lifter B. Weight lifter A lifts 368 pounds 368 + 104 = 472 Therefore, Weight Lifter B lifts the most weight.

Circle the value of the underlined digit.

Model the equation. Draw your model. Then find the sum. 195 + 308 = ___

Answer: 195 = 100 + 90 + 5 308 = 300 + 00 + 8 503 = 400 + 90 + 13

Reasoning How can you use an estimate to check whether your answer reasonable?

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 195 = 200 308 = 300 200 +300 500 Ths sum is about 500. Step 2: Find the sum. Add the ones, tens, then the hundreds. 195 +308 503 503 is close to 500. So, the answer is reasonable.

Think and Grow: Add Three-Digit Numbers

Find the sum. Check whether your answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 457 – 500 133 – 100 500 +100 600 The sum is about 600. Step 2: Find the sum. Add the ones, tens, then the hundreds. 457 +133  590 590 is close to 600. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 269 – 300 354 – 300 300 +300 300 Step 2: Find the sum. Add the ones, tens, then the hundreds. 269 +354 623 623 is close to 600. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 560 – 600 274 – 300 600 +300 900 Step 2: Find the sum. Add the ones, tens, then the hundreds. 560 +274  834 834 is close to 900. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 345 – 300 286 – 300 300 +300 600 Step 2: Find the sum. Add the ones, tens, then the hundreds. 345 +286 631 631 is close to 600. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 129 – 100 668 – 700 100 +700 800 Step 2: Find the sum. Add the ones, tens, then the hundreds. 129 +668 797 797 is close to 800. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 383 – 400 539 – 500 400 +500 900 Step 2: Find the sum. Add the ones, tens, then the hundreds. 383 +539 922 922 is close to 900. So, the answer is reasonable.

Apply and Grow: practice

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 803 – 800 179 – 200 800 +200 1000 Step 2: Find the sum. Add the ones, tens, then the hundreds. 803 +179 982 982 is close to 1000. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 608 – 600 239 – 200 600 +200 800 Step 2: Find the sum. Add the ones, tens, then the hundreds. 608 +239 847 847 is close to 800. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 427 – 400 385 – 400 400 +400 800 Step 2: Find the sum. Add the ones, tens, then the hundreds. 427 +385 812 812 is close to 800. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 401 – 400 109 – 100 400 +100 500 Step 2: Find the sum. Add the ones, tens, then the hundreds. 401 +109 510 510 is close to 500. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 265 – 300 157 – 100 300 +100 400 Step 2: Find the sum. Add the ones, tens, then the hundreds. 265 +157 422 422 is close to 400. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 375 – 400 64 – 100 400 +100 500 Step 2: Find the sum. Add the ones, tens, then the hundreds. 375 +64 439 439 is close to 500. So, the answer is reasonable.

Question 13. Estimate: ___ 469 + 284 = ___

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 469 – 500 284 – 300 500 +300 800 Step 2: Find the sum. Add the ones, tens, then the hundreds. 469 +284  753 753 is close to 800. So, the answer is reasonable.

Question 14. Estimate: ___ 580 + 246 = __

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 580 – 600 246 – 200 600 +200 800 Step 2: Find the sum. Add the ones, tens, then the hundreds. 580 +246 826 826 is close to 800. So, the answer is reasonable.

Question 15. Estimate: ___ 796 + 135 = ___

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 796 – 800 135 – 100 800 +100 900 Step 2: Find the sum. Add the ones, tens, then the hundreds. 796 +135 931 931 is close to 900. So, the answer is reasonable.

Question 16. A truck driver travels 428 miles on Monday. He travels 473 miles on Tuesday. How many miles does he travel in all on Monday and Tuesday?

Answer: Given that, A truck driver travels 428 miles on Monday. He travels 473 miles on Tuesday. 428 +473 901 Thus he travels 901 miles on Monday and Tuesday.

Answer: 119 + 187 306 Your answer is not reasonable.

Answer: Given, A construction team builds an 825-meter-long boardwalk on a beach. The team builds 408 meters one week and 377 meters the next week. 408 +377 785 The boardwalk did not complete.

Question 18. A road crew repaves the road on a 547-meter-long bridge. The crew repaves 318 meters the first day and 229 meters the second day. Is the road on the bridge completely repaved?

Answer: Given, A road crew repaves the road on a 547-meter-long bridge. The crew repaves 318 meters on the first day and 229 meters on the second day. 318 +229 547 Yes, the road on the bridge completely repaved.

Question 19. A family drives from St. Louis to Orlando for a vacation. The family drives 363 miles the first day and 386 miles the second day. How many miles does the family have left to drive?

Answer: Day 1 – 468 + 527 = 995 Day 2 – 416 + 374 = 790 995 – 790 = 205 Thus day 1 has more visitors in all.

Find the sum. Check whether your answer is answerable.

Answer: 630

Explanation: The estimated number of 493 is 490 The estimated number of 142 is 140. 490 + 140 630

Answer: 820

Explanation: The estimated number of 763 is 760. The estimated number of 58 is 60. 760 + 60 820

Answer: 580

Explanation: The estimated number of 308 is 310 The estimated number of 273 is 270 310 +270 580

Answer: 420

Explanation: The estimated number of 276 is 280 The estimated number of 138 is 140 280 + 140 420

Answer: 700

Explanation: The estimated number of 532 is 530 The estimated number of 167 is 170. 530 +170 700

Answer: 980

Explanation: The estimated number of 680 The estimated number of 296 is 300. 680 +300 980

Question 7. Estimate: ___ 595 + 280 = ___

Answer: 880

Explanation: The estimated number of 595 is 600 The estimated number of 280 600 + 280 880

Question 8. Estimate: ___ 419 + 295

Answer: 720

Explanation: The estimated number of 419  is 420 The estimated number of 295 is 300 420 + 300 720

Question 9. Estimate: ___ 498 + 305 = ___

Answer: 800

Explanation: The estimated number of 498 is 500 The estimated number of 305 is 300 500 +300 800

Answer: Let the addend be 3 479 +283 762 If you take 3 as addend then you need to regroup to find the sum. Let the addend be 9 697 +135 832 If you take 9 as addend then you need to regroup to find the sum.

Question 12. Modeling Real Life Newton wants to complete a 770-mile hike in 2 months. He hikes 423 miles the first month and 347 miles the second month. Does he complete the hike?

Answer: Given, Newton wants to complete a 770-mile hike in 2 months. He hikes 423 miles the first month and 347 miles the second month 423 +347 770 Thus he Newton completed the hike.

Answer: Given, You ship a package 750 miles from San Diego to Salt Lake City. The package is now in Las Vegas. 121 + 270 = 391 miles until Las Vegas. 750 – 391 = 359 miles Therefore 359 miles are left until your package is delivered.

Find the quotient.

Explanation: Divide the two numbers 100 and 10. 100/10 = 10 Thus the quotient is 10.

Explanation: Divide the two numbers 45 and 5. 45/5 = 9 Thus the quotient is 9.

Explanation: Divide the two numbers 14 and 7. 14/2 = 7 Thus the quotient is 7.

Explanation: Divide the two numbers 10 and 80. 80/10 = 8 Thus the quotient is 8.

Question 18. Divide 25 by 5.

Explanation: Divide the two numbers 5 and 25. 25/5 = 5 Thus the quotient is 5.

Question 19. Divide 30 by 10.

Explanation: Divide the two numbers 10 and 30. 30/10 = 3 Thus the quotient is 3.

Question 20. Divide 8 by 2.

Explanation: Divide the two numbers 8 and 2. 8/2 = 4 Thus the quotient is 4.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 348 = 350 478 = 480 152 = 150 350 + 480 + 150 = 980 The sum is about 980. 517 = 520 117 = 120 283 = 280 520 + 120 + 280 = 920 The sum is about 920 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 348 +478 +152 978 978 is close to 980. So, the answer is reasonable. 517 +117 +283 917 917 is close to 920, So, the answer is reasonable.

Reasoning Why did you choose those numbers? Compare your strategy to your partner’s strategy.

Answer: 348 = 350 478 = 480 152 = 150 I choose these numbers because they are nearest to ten. This strategy will help to improve the mental math. After solving the problem you can verify the answer with the actual sum.

Think and Grow: Add Three or More Numbers

Answer: Step 1: Estimate. Round each addend to the nearest ten. 140 + 220 + 180 + 90 = 630 The sum is about 630. Step 2: Find the sum, add the ones, then the tens, then the hundreds. 138 +221 +176 +92 627 627 is close to 630. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 342 = 340 73 = 70 267 = 270 340 + 70 + 270 = 680 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 342 +73 +267 682 682 is close to 680. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 65 = 60 98 = 100 637 = 640 640 +100 +60 800 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 637 +98 +65 800 800 is close to 800. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 382 = 380 357 = 360 160 + 380 + 360 = 900 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 160 382 357 899 899 is close to 900. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 35 = 30 68 = 70 827 = 830 30 + 70 + 830 = 930 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 35 + 68 + 827 = 930 930 is close to 930. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 153 = 150 235 = 230 458 = 460 67 = 70 150 + 230 + 460 + 70 = 910 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 153 + 235 + 458 + 67 = 913 913 is close to 910. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 108 = 110 172 = 170 200 = 200 263 = 260 110 + 170 + 200 + 260 = 740 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 108 + 172 + 200 + 263 = 743 743 is close to 740. So, the answer is reasonable.

Answer: Step 1: Estimate. Round each addend to the nearest ten. 181 = 180 629 = 630 140 = 140 23 = 20 180 + 630 + 140 + 20 = 970 Step 2: Find the sum, add the ones, then the tens, then the hundreds. 181 + 629 + 140 + 23 = 973 973 is close to 970. So, the answer is reasonable.

Question 16. Number Sense Use the Associative Property of Addition to find (345 + 234) + 206.

Answer: We can find the (345 + 234) + 206 by using the Associative Property of Addition. (a + b) + c = a + (b + c) (345 + 234) + 206 = 345 + (234 + 206) 345 + 440 = 785

Answer: Your friend is incorrect. The order of the sum is wrong. 27 is placed in the wrong pattern. 2 and 7 must be places on tens place and ones place. 364 109 +27 503

Understand the problem: Make a plan: Solve: He ___ bring all 3 boxes on the elevator at once.

Answer: Given that, An elevator has a weight limit of 1,000 pounds. A 186-pound man has three 265-pound boxes to deliver. 265 + 265 + 265 + 186 = 981 1000 – 981 = 19 pounds Thus he can bring all 3 boxes on the elevator at once.

Question 18. An auditorium has 650 seats. 175 students from each of 3 schools compete in a math competition. 68 teachers assist. Are there enough seats for all of the students and teachers?

Answer: Given, An auditorium has 650 seats. 175 students from each of 3 schools compete in a math competition. 68 teachers assist. 175 + 175 + 175 + 68 = 593 Thus the seats are enough for all of the students and teachers.

Answer: Add the number of signatures of all the students A  + B + C + D = 77 + 108 + 112 + 96 = 393 500 – 393 = 107 Thus they need 107 signatures more.

Find the sum. Check whether your answer is reasonable

Answer: Step 1: Estimate. Round each addend to the nearest ten. Step 2: Find the sum, add the ones, then the tens, then the hundreds. 862 is close to 860. So, the answer is reasonable.

Question 8. Reasoning You add 602 + 125 + 231. Your friend adds 231 + 602 + 125. Do you both get the same answer? Use an additional property to explain.

Answer: There are four mathematical properties that involve addition. The properties are the commutative, associative, additive identity and distributive properties. Additive Identity Property: The sum of any number and zero is the original number. 602 + 125 + 231 = 958 231 + 602 + 125 = 958 The sum will be the same irrespective of the change of order.

Answer: A firefighter’s ladder has a weight limit of 750 pounds. One firefighter weighs 196 pounds. Another firefighter weighs 243 pounds. They each have 67 pounds of gear. 196 + 243 + 67 + 67 = 573 750 – 573 = 177 pounds If both firefighters wear their gear, they can climb the ladder at the same time.

Answer: Given, Your principal agrees to make a lip-sync video if the school’s social media page reaches 1,000 likes in 5 days. Add all the number of likes 573 + 168 + 201 + 47 = 989 1000 – 989 = 19 likes Thus the school’s page needs 19 likes more.

Answer: From the figure, we can observe that each block = 1 sq. cm We have to find the area of the shaded part. The shaded region is in the form of a rectangle. So, we have to find the area of the rectangle. A = l × b A = 7 × 3 A = 21 sq.cm Thus the area of the shape is 21 sq. cm

Reasoning How can finding 79 – 47 help you find 379 – 47?

Answer: You can subtract 47 from 79 by using the number line. 79 – 47 = 32 Just add 300 to 79 or add 3 to the left and subtract 47 from 379. 379 – 47 = 332

Think and Grow: Subtracting on a Number Line

Find the difference.

Question 7. Your friend knows 154 words in Italian. You want to know just as many words as your friend. So far, you have learned 73 words. How many words do you have left to learn?

Answer: Given, Your friend knows 154 words in Italian. You want to know just as many words as your friend. So far, you have learned 73 words. 154 – 73 = 81 Thus 81 words are left to learn.

Answer: By seeing the above number line we can find the subtraction equation. Use the count on strategy. Start at 36. Count on until you reach 407. 407 – 36 = 371

Answer: Given, A marine biologist feeds 435 pounds of fish to an orca and 50 pounds of fish to a sea lion. 435 – 50 = 385 Thus 385 more pounds the orca eat than the sea lion.

Question 10. There are 620 paper lanterns for a festival. Some are let go. There are 42 left. How many paper lanterns were let go?

Answer: Given, There are 620 paper lanterns for a festival. Some are let go. There are 42 left. 620 – 42 = 578 Therefore 578 paper lanterns were let go.

Question 11. DIG DEEPER! There are some guests at an amusement park. 387 of them leave when it rains. 474 of them stay. How many guests were there before it rained?

Answer: Given that, There are some guests at an amusement park. 387 of them leave when it rains. 474 of them stay. 387 + 474 = 861 Thus 861 guests were there before it rained.

Find the difference

Question 5. Writing Write and solve a subtraction word problem using 995 and 238.

Answer: Among all the number lines option ii is used to find 734 – 308.

Answer: Given that, You take 107 pictures on a field trip to a zoo. Your friend takes 73 pictures. 107 – 73 = 34 You take 34 pictures than your friend.

Question 8. Modeling Real Life An author has 350 copies, not of her book. Some are signed. 115 copies are signed. How many copies are signed?

Answer: Given, An author has 350 copies, not of her book. Some are signed. 115 copies are signed. 350 – 115 = 235 copies Therefore 235 copies are to be signed.

Question 9. Divide 25 by 5.

Explanation: Divide the two numbers 25 and 5. 25/5 = 5 Thus the quotient is 5.

Question 10. Divide 40 by 4.

Explanation: Divide the two numbers 40 and 4. 40/4 = 10 Thus the quotient is 10.

Question 11. Divide 72 by 8.

Explanation: Divide the two numbers 72 and 8. 72/8 = 9 Thus the quotient is 9.

750 – 300 = ___ 650 – 200 = ____ 750 – 300 = ___ 700 – 250 = ____ 750 – 300 = ___ 740 – 290 = ____

What patterns do you notice? Explain.

Answer: 750 – 300 = 450 650 – 200 = 450 750 – 300 = 450 700 – 250 = 450 750 – 300 = 450 740 – 290 = 450 Here you notice that all the answers are 450 for different patterns.

Think and Grow: Mental Math Strategies for Subtraction

Use compensation to find the difference

Use mental math to find the difference

Question 6. 643 – 115 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 643 + 5 = 648 115 + 5 = 120 648 -120 528 So, 643 – 115 = 528

Question 7. 863 – 257 = ___

Answer: Use compensation to change both numbers. Add 3 to both numbers and use mental math strategy. 863 + 3 = 866 257 + 3 = 260 866 -260 606

Question 8. 768 – 543 = ___

Answer: Use compensation to change both numbers. Add 2 to both numbers and use mental math strategy. 768 + 2 = 770 543 + 2 = 545 770 -545 225

Question 9. 688 – 414 = ___

Answer: Use compensation to change both numbers. Add 1 to both numbers and use mental math strategy. 688 + 1 = 689 414 + 1 = 415 689 -415 274

Question 10. 499 – 106 = ___

Answer: Use compensation to change both numbers. Add 4 to both numbers and use mental math strategy. 499 + 4 = 503 106 + 4 = 110 503 -110 393

Question 11. 495 – 162 = ___

Answer: Use compensation to change both numbers. Add 3 to both numbers and use mental math strategy. 495 + 3 = 498 162 + 3 = 165 498 -165 333

Question 12. 874 – 515 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 874 + 5 = 879 515 + 5 = 520 879 -520 359

Question 13. 637 – 228 = ___

Answer: Use compensation to change both numbers. Add 2 to both numbers and use mental math strategy. 637 + 2 = 639 228 + 2 = 230 639 -230 409

Question 14. 986 – 432 = ___

Answer: Use compensation to change both numbers. Add 3 to both numbers and use mental math strategy. 986 + 3 = 989 432 + 3 = 435 989 -435 554

Answer: Given that, A movie theater has 225 seats. 108 seats are not taken. 225 – 108 = 117 Therefore 117 seats are not taken.

Answer: The next step is to subtract the original numbers. 741 -295 446

Subtraction equation: Compare: The coach ___ has enough money to buy the bat.

Answer: Given A softball coach has $325 for new equipment. She buys the catching gear. 325 + 1 = 326 219 + 1 = 220 326 -220 106 The cost of the bat is $109. Thus she does not have enough money.

Question 17. A store owner has 550 T-shirts. He sells 333 of them. Then he receives an order for 168 T-shirts. Does he have enough T-shirts to complete the order?

Answer: Given that, A store owner has 550 T-shirts. He sells 333 of them. 550 – 333 = 217 Then he receives an order for 168 T-shirts. 217 – 168 = 49 Yes, he has enough T-shirts to complete the order.

Answer: Given that, The manager of a gaming center has $700 for new electronics. She buys the game system. $399 + $169 = $568 700 – 568 = $132 Thus she has enough money left for either of the other two items. She can buy the game system and a bundle of games.

DIG DEEPER! How much more money does the manager need to buy both the television and the bundle of games?

Answer: The cost of television is $379 The cost of the bundle of games = $169 379 + 169 = 548 Thus the manager need $548 to buy both the television and the bundle of games

Use compensation to find the difference.

Answer: Use compensation to change both numbers. Add 3 to both numbers and use mental math strategy. 596 + 3 = 599 317 + 3 = 320 599 -320 279 So, 596 – 317 = 279

Answer: Add 6 to 214 to make the subtraction easier. 685 -214 + 6 = 220 685 -220 465 So, 685 – 214 = 465

Use mental math to find the difference.

Question 3. 782 – 489 = ___

Answer: Use compensation to change both numbers. Add 1 to both numbers and use mental math strategy. 782 + 1 = 783 489 + 1 = 490 783 -490 293 So, 782 – 489 = 293

Question 4. 672 – 266 = ___

Answer: Use compensation to change both numbers. Add 4 to both numbers and use mental math strategy. 672 + 4 = 676 266 + 4 = 270 676 -270 406 So, 672 – 266 = 406

Question 5. 983 – 155 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 983 + 5 = 988 155 + 5 = 160 988 -160 820 So, 983 – 155 = 820

Question 6. 744 – 125 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 744 + 5 = 749 125 + 5 = 130 749 – 130 619 So, 744 – 125 = 619

Question 7. 967 – 619 = ___

Answer: Use compensation to change both numbers. Add 1 to both numbers and use mental math strategy. 967 + 1 = 968 619 + 1 = 620 968 -620 348 So, 967 – 619 = 348

Question 8. 854 – 517 = ___

Answer: Use compensation to change both numbers. Add 3 to both numbers and use mental math strategy. 854 + 3 = 857 517 + 3 = 520 857 -520 337 So, 854 – 517 = 337

Question 9. 472 – 215 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 472 + 5 = 479 215 + 5 = 220 479 – 220 259 So, 472 – 215 = 259

Question 10. 883 – 335 = ___

Answer: Use compensation to change both numbers. Add 5 to both numbers and use mental math strategy. 883 + 5 = 888 335 + 5 = 340 888 -340 548 So, 883 – 335 = 548

Question 11. 575 – 198 = ___

Answer: Use compensation to change both numbers. Add 2 to both numbers and use mental math strategy. 575 + 2 = 577 198 + 2 = 200 577 -200 377 So, 575 – 198 = 377

Question 12. Reasoning To find 765 – 246, Newton adds 5 to each number and then subtracts. To find the difference, Descartes adds 4 to each number, and then subtracts. Will they both get the correct answer? Explain.

Answer: Given, To find 765 – 246, Newton adds 5 to each number and then subtracts. 765 + 5 = 770 246 + 5 = 251 770 – 251 = 519 To find the difference, Descartes adds 4 to each number, and then subtracts. 765 + 4 = 769 246 + 4 = 250 769 – 250 = 519 Yes they both get the correct answer.

Question 13. Modeling Real Life A custodian has 350 desks to clean. She cleans 124 desks on the first floor and 147 desks on the second floor. Does she clean all of the desks?

Answer: Given that, A custodian has 350 desks to clean. She cleans 124 desks on the first floor and 147 desks on the second floor. 124 + 147 = 271 350 -271 79 No, she did not clean all of the desks.

Answer: Given, A fashion designer has $ 725 to spend on new supplies. She buys the sewing machine. 725 – 495 = 230 Yes she has enough money left for either of the other two items She can buy a Mannequin.

DIG DEEPER! How much more money does the fashion designer need to buy both the mannequin and the fashion design software?

Answer: Given, The cost of the Mannequin is $129 The cost of the fashion design software is $329 129 + 329 = 458 458 – 230 = 228 Thus she needs 228 to buy both the mannequin and the fashion design software.

Draw equal groups. Then complete the equations.

Answer: 3 groups of 6 means 3 times 6. 6 + 6 + 6 = 18 3 × 6 = 18

Answer: 4 groups of 9 means 4 times 9. 9 + 9 + 9 + 9 = 36 4 × 9 = 36

Model the equation. Draw to show your model. Then find the difference. 694 – 418 = ___

Reasoning How can you use an estimate to check whether your answer is reasonable?

Think and Grow: Subtract Three-Digit Numbers

Find the difference. Check whether your answer is reasonable.

Question 13. Estimate: ____ 552 – 381 = ___

Question 14. Estimate: ___ 725 – 146 = ____

Question 15. Estimate: ___ 800 – 486 = ___

Answer: Given that, The number of rings on a tree is equal to its age. A redwood tree has 473 rings. A bristlecone pine tree has 806 rings 806 -473 333 Thus 333 older is the bristlecone pine tree than the redwood tree.

Question 17. Writing Explain how to regroup 408 to subtract 259.

Answer: Working each column from right to left 9 is greater than 8 so you must regroup: Take 1 from 4, so 4 becomes 3. Add 10 to 0, so 0 becomes 10. Take 1 from 10, so 10 becomes 9. Add 10 to 8, so 8 becomes 18. 18 minus 9 is 9. 9 minus 5 is 4. 3 minus 2 is 1. 408 -259 149

Answer: 800 -444 356 The class needs to collect 356 more pennies.

Answer: Total summer camp openings = 405 Filled = 316 400 – 316 = 84 84 more campers can attend the summer camp.

Question 19. A musician wants to buy a set of speakers that costs $672. She saves $224 each month for 2 months. How much money does she still need to save?

Answer: Given that, A musician wants to buy a set of speakers that costs $672. She saves $224 each month for 2 months. 224 + 224 = 448 672 – 448 = 224 Thus she still need to save $224.

Answer: Given, Newton has 442 packages to deliver. Descartes has 464. Newton delivers 174 packages, and Descartes delivers 188. 442 – 174 = 268 464 – 188 = 276 Thus Newton is closer to finishing his deliveries.

Question 4. Estimate: ___ 690 – 298 = ___

Question 5. Estimate: ___ 613 – 472 = ___

Question 6. Estimate: ___ 835 – 189 = ___

Question 7. YOU BE THE TEACHER Your friend says you have to regroup every time you subtract from a number that has a zero. Is your friend correct? Explain.

Answer: Your friend says you have to regroup every time you subtract from a number that has a zero. Yes, your friend is correct. Because whenever you subtract a number from 0 you have to regroup.

Answer: To find how many more soup can label does the school need to reach the goal you have to subtract label collected from school soup. 1000 – 638 = 362

Question 9. Modeling Real Life Newton wants to buy a couch that costs $594. He saves $198 each month for 2 months. How much money does he still need to save?

Answer: Given, Newton wants to buy a couch that costs $594. He saves $198 each month for 2 months. 198 × 2 = $396 594 – 396 = -198 Therefore Newton need to save $198 to buy the couch.

Round the number to the nearest ten and to the nearest hundred.

Answer: The number 64 nearest ten is 60. The number nearest hundred to 64 is 60.

Answer: The number 411 nearest ten is 410 The number nearest hundred to 411 is 400.

Reasoning How are addition and subtraction related?

Answer: 497 – 358 = 136 Check the answer by using the addition model. 136 +358 497 So, the answer is reasonable.

Think and Grow: Relate Addition and Subtraction

Find the sum or difference. Use the inverse operation to check.

Answer: First, add 463 from 349 and then use the inverse operation to check the solution. 463 +349 812 Use the inverse operation to check the solution 812 -349 463 So, the answer is reasonable.

Answer: First, subtract 790 from 317 and then use the inverse operation to check the solution. 790 -317 473 Use the inverse operation to check the solution 473 +317 790 So, the answer is reasonable.

Answer: First, subtract 857 from 567 and then use the inverse operation to check the solution. 857 -567 290 Use the inverse operation to check the solution 290 +567 857 So, the answer is reasonable.

Answer: First, add 762 from 143 and then use the inverse operation to check the solution. 762 +143 905 Use the inverse operation to check the solution 905 -143 762 So, the answer is reasonable.

Answer: First, add 653 from 217 and then use the inverse operation to check the solution. 653 +217 870 Use the inverse operation to check the solution 870 -217 653 So, the answer is reasonable.

Answer: First, subtract 294 from 156 and then use the inverse operation to check the solution. 294 -156 138 Use the inverse operation to check the solution 138 +156 294 So, the answer is reasonable.

Answer: First, add 475 from 438 and then use the inverse operation to check the solution. 475 +438 913 Use the inverse operation to check the solution 913 -438 475 So, the answer is reasonable.

Answer: First, subtract 514 from 386 and then use the inverse operation to check the solution. 514 -386 128 Use the inverse operation to check the solution 128 +386 514 So, the answer is reasonable.

Answer: The fourth equation does not belong with the other three. Because it is not using the inverse operation of addition and subtraction.

Question 14. Open-Ended Write a subtraction equation that has a difference of 381.

Answer: 901 – 520 = 381 Take the number on your own and write the subtraction equation with the difference of 381.

Answer: Given that, A kayak costs $321. A customer pays $196 for the kayak after using a gift card. 321 – 196 = 125 Thus the gift card worth $125.

Question 15. You print 600 flyers for an event. You hand out some of them. There are 237 left. How many flyers did you hand out?

Answer: Given that, You print 600 flyers for an event. You hand out some of them. There are 237 left. 600 – 237 = 363 Thus you hand out 363 flyers. 363 + 237 = 600

Question 16. A building has 163 floors. You start on the 28th floor. You go up in the elevator 126 floors. Then you go down 145 floors. On which floor do you end?

Answer: Given that, A building has 163 floors. You start on the 28th floor. You go up in the elevator 126 floors. Then you go down 145 floors. 126 – 28 = 98 floors 145 – 98 = 47 Thus you end at 47th floor.

Answer: Given that, A bus travels from Boston to Washington, D.C. On the way back, the bus stops in New York City. We have to find How many miles has the bus traveled in all 441 + 225 = 666 miles Thus a bus travels 666 miles. 666 – 225 = 441 miles

Answer: 931 -544 387 Now you have to do the inverse operation. 387 +544 931

Answer: 623 +285 908 Now you have to do the inverse operation. 908 -285 623

Answer: 523 +237 760 Now you have to do the inverse operation. 760 -237 523

Answer: 403 -252 151 Now you have to do the inverse operation. 151 +252 403

Answer: 612 +387 999 Now you have to do the inverse operation. 999 -387 612

Answer: 511 -371 140 Now you have to do the inverse operation. 140 +371 511

Answer: 437 +156 593 Now you have to do the inverse operation. 593 -156 437

Answer: 726 -362 364 Now you have to do the inverse operation. 364 +362 726

Answer: No, your friend is incorrect. 380 -159 221 Now you have to do the inverse operation. 221 +159 380

Answer: 208 + 475 = 683 Now you have to do the inverse operation. 683 – 475 = 208 The second figure does not belong to the other three expressions.

Question 11. Modeling Real Life A telescope costs $169. A customer pays $119 for the telescope after using a gift card. How much money is the gift card worth?

Answer: Given that, A telescope costs $169. A customer pays $119 for the telescope after using a gift card. 169 -119 50 The cost of the gift card is $50.

Answer: Given, A train travels from Dallas to San Antonio. On the way back, the train stops in Austin. 274 – 79 = 195 miles The train has traveled 195 miles. 79 miles left to travel from Austin to San Antonio.

Answer: 4 × 8 = 4 × (4 + 4) 4 × 8 = (4 × 4) + (4 × 4) 4 × 8 = 16 +16 4 × 8 = 32 Thus the area of the rectangle = 32 square foot.

what does p represent? p = ___

Answer: Let 9 be the number of pages read 56 + 47 + p = 150 103 + p = 150 p = 150 – 103 p = 47

Construct Arguments Explain to your partner how to find what n represents. 250 + n = 580

Answer: Given the expression 250 + n = 580 n = 580 – 250 n = 330

Think and Grow: Using the Problem-Solving Plan Example Newton has 368 baseball cards. He gives away 139 of them. He buys 26 more. How many cards does he have now?

Understand the Problem

• Newton has ___ cards.
• He gives away of them.
• He buys ___ more.
• You need to find how many ___ he has now.
• Newton has 368 cards.
• He buys 26  more.
• You need to find how many cards he has now.

Make a Plan

How will you solve?

• Subtract ___ from ___ to find how many ___ he has left after he gives some away.
• Then add ___ to the difference to find how many he has now.
• Subtract 139 from 368 to find how many cards he has left after he gives some away.
• Then add 26 to the difference to find how many he has now.

Newton has __ cards now.

Answer: Step 1: c is the unknown difference. 368 – 139 = c c = 229 Step 2: c = 229 229 + 26 = n n = 225 Thus the unknown sum is 225.

Question 1. Explain how you can check whether your answer above is reasonable.

Answer: You can check the answer by using addition and subtraction. 368 -139 229 Now check whether the answer is correct or not. 229 +139 368 So, the answer is reasonable.

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.

Question 2. A baker makes 476 muffins. He sells 218 of them. Then he makes 390 more. How many muffins does the baker have now?

Answer: Given, A baker makes 476 muffins. He sells 218 of them. 476 -218 258 Then he makes 390 more. 390 +258 648 Thus the baker has 348 muffins now.

Question 3. Newton knocks down 146 pins in his first bowling game. He knocks down 19 more pins in his second game than in his first game. How many pins does he knock down in all?

Answer: Given that, Newton knocks down 146 pins in his first bowling game. He knocks down 19 more pins in his second game than in his first game. 146 +19 165 He knocks down 165 pins in his second game. To find the total number of pins we have to the points in the first game and second game. 146 +165 311 Thus he knockdowns 311 pins in all.

Question 4. You are traveling to a campground that is 243 miles away. You travel 155 miles in the morning and 59 miles in the afternoon. How many more miles do you need to travel before you get to the campground?

Answer: Given that, You are traveling to a campground that is 243 miles away. You travel 155 miles in the morning and 59 miles in the afternoon. 155 +59 214 243 -214 029 Thus you need to travel 29 miles to get to the campground.

Question 5. There are 205 lawn tickets and 585 bleacher tickets sold for a concert. There are 680 fewer VIP tickets sold than lawn and bleacher tickets combined. How many VIP tickets are sold?

Answer: Given, There are 205 lawn tickets and 585 bleacher tickets sold for a concert. 205 + 585 = 790 There are 680 fewer VIP tickets sold than lawn and bleacher tickets combined. 790 -680 110 Thus 110 VIP tickets are sold.

Answer: Thursday – 346 people Saturday – 512 people 346 + 512 = 858 people 897 -858 39 39 more people went to see the movie on Friday than on Thursday and Saturday combined.

Answer: Friday – 903 passengers Saturday – 624 passengers Sunday – 255 passengers 624 +255 879 Now subtract 879 from 903. 903 -879 024

Question 1. Newton has 387 tokens, and Descartes has 295. They use a total of 461 tokens. How many tokens do they have now?

Answer: 222 tokens

Explanation: Given that, Newton has 387 tokens, and Descartes has 295. 387 + 295 = 682 They use a total of 461 tokens. 682 – 461 = 222 tokens Thus they have 222 tokens now.

Question 2. There are 125-second graders and 118 third graders at a museum. There are 249 more adults than students at the museum. How many adults are at the museum?

Answer: Given that, There are 125-second graders and 118 third graders at a museum. 125 + 118 = 243 graders There are 249 more adults than students at the museum. 243 + 249 = 492 Therefore 492 adults are at the museum.

Question 3. You received 171 votes in a coloring contest. Your friend received 24 fewer votes than you. How many people voted for you and your friend in all?

Answer: Given, You received 171 votes in a coloring contest. Your friend received 24 fewer votes than you. 171 + 24 = 195 votes The number of votes for your friend is 195. 171+ 195 = 366 votes Thus 366 people voted for you and your friend.

Question 4. Writing Write and solve a two-step problem that can be solved using addition or subtraction.

Answer: You bought 10 packs of sketches and your friend bought 4 packs less than you. Each pack contains 10 sketches. Find how many sketches you and your friend bought in all. Sol: You bought 10 packs of sketches and your friend bought 4 packs less than you. 10 – 4 = 6 packs Your friend bought 6 packs. Each pack contains 10 sketches. 10 + 6 = 16 16 × 10 = 160 Thus you and your friend bought 160 sketches.

Answer: Number of fish caught on Friday and Saturday = 127 + 244 = 371 Number of fish caught on Sunday = 564 564 – 371 = 193 193 more fish were caught on Sunday than on Friday and Saturday combined.

Answer: The pattern shows that it is the multiple of 5. 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25

Your school holds a talent show.

Question 1. You and your friend hand out programs to guests before the show. You each start with 250 programs. There are 114 programs left. How many programs did you and your friend hand out?

Answer: 250 – 114 = 136 programs Thus you and your friend hand out 136 programs. 136 + 114 = 250 programs

Answer: Given, 75 students wait backstage to perform in the show. There are 336 children, 125 adults, and 14 teachers in the audience. 75 + 336 + 125 + 14 = 550 Thus there are 550 people are in the talent show.

Answer: 16 students

Explanation: Given, Four students perform in each of the first 4 acts. 4 × 4 = 16 Thus 16 students need to perform.

c. Each performer is given a juice box backstage. Juice boxes come in packages of 10. How many packages did the teachers buy? How many juice boxes are left?

Answer: Given, Each performer is given a juice box backstage. Juice boxes come in packages of 10. 1 box – 10 packages 16 × 1 = 16 boxes 16 × 10 = 160 packages

Three in a Row: Addition and Subtraction

Answer: Sums: 547 + 107 = 654 547 + 338 = 885 547 + 262 = 809 I got the three counters vertically.

8.1 Identify Addition Properties

Question 1. 59 + 0 = 59

Answer: It shows the Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 2. (14 + 32) + 6 = 14 + (32 + 6)

Question 3. 27 + 51 = 51 + 27

Answer: Commutative Property of addition Changing the grouping of addends does not change the sum.

Answer: 64 + 12 = 12 + 64 – Commutative Property of addition changing the grouping of addends does not change the sum. 71 + 0 = 71 – It shows the Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number. (56 + 21) + 34 = 56 + (21 + 34) – It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum. 26 + (41 + 4) = 4 + (26 + 41) – It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

8.2 Use Number Lines to Add

8.3 Use Mental Math to Add

Question 6. 192 + 107 = ___

Answer: You can find the sum of 192 and 107 by using mental math strategies. 192 – 2 = 190 107 + 2 = 109 190 +109 299

Question 7. 676 + 114 = ___

Answer: You can find the sum of 676 and 114 by using mental math strategies. 676 + 4 = 680 114 – 4 = 110 680 +110 790

Question 8. 716 + 279 = ___

Answer: You can find the sum of 716 and 279 by using mental math strategies. 716 – 1 = 715 279 + 1 = 280 715 +280 995

Question 9. 501 + 468 = ___

Answer: You can find the sum of 501 and 468 by using mental math strategies. 501 – 1 = 500 468 + 1 = 469 500 +469 969

Question 10. 527 + 343 = ___

Answer: You can find the sum of 527 and 343 by using mental math strategies. 527 + 3 = 530 343 – 3 = 340 530 +340 870

Question 11. 441 + 189 = ___

Answer: You can find the sum of 441 and 189 by using mental math strategies. 441 – 1 = 440 189 + 1 = 190 440 +190 630

8.4 Use Partial Sums to Add

Answer: 586 = 500 + 80 + 6 107 = 100 + 00 + 7 693 = 600 + 80 + 13

Answer: 647 = 600 + 40 + 7 293 = 200 + 90 + 3 940 = 800 + 130 + 10

Answer: Given, On Earth, your cousin weighs 207 pounds less than he would on Jupiter. Your cousin weighs 135 pounds on Earth. 207 + 135 = 342 Thus your cousin would weigh 342 pounds on Jupiter.

8.5 Add Three-Digit Numbers

Question 15. Estimate: ___ 326 + 490 = ___

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 326 = 300 490 = 500 300 + 500 = 800 The sum is about 800. Step 2: Find the sum. Add the ones, tens, then the hundreds. 326 +490 816 816 is close to 800. So, the answer is reasonable.

Question 16. Estimate: ___ 657 + 189 = ___

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 657 = 700 189 = 200 600 + 200 = 800 The sum is about 800. Step 2: Find the sum. Add the ones, tens, then the hundreds. 657 + 189 = 846 846 is close to 800. So, the answer is reasonable.

Question 17. Estimate: ___ 543 + 261 = ___

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 543 = 500 261 = 300 500 + 300 = 800 The sum is about 800. Step 2: Find the sum. Add the ones, tens, then the hundreds. 543 + 261 = 804 804 is close to 800. So, the answer is reasonable.

8.6 Add Three or More Numbers

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 78 = 100 433 = 400 367 = 400 100 + 400 + 400 = 900 The sum is about 900.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 194 = 200 151 = 200 244 = 200 231 = 200 200 + 200 + 200 + 200 = 800 The sum is about 800.

Answer: Step 1: Estimate. Round each addend to the nearest hundred. 373 = 400 329 = 300 118 = 100 61 = 100 400 + 300 + 100 + 100 = 900 The sum is about 900.

8.7 Use Number Lines to Subtract

Answer: By seeing the above number we can find the subtraction equation. 764 – 50 = 714 714 – 4 = 710 710 – 3 = 707 The subtraction equation is 764 – 57 = 707

8.8 Use Mental Math to Subtract

Question 23. 957 – 619 = ___

Answer: 957 – 7 = 950 619 + 7 = 626 950 -626 324 The difference is 324.

Question 24. 831 – 415 = ___

Answer: 831 – 1 = 830 415 + 1 = 416 830 -416 414 The difference is 414.

Question 25. 876 – 366 = ___

Answer: 876 – 6 = 870 366 + 6 = 372 870 – 372 = 498

Question 26. 636 – 317 = ___

Answer: 636 + 6 = 642 317 – 6 = 311 642 – 311 = 331 The difference is 331.

Question 27. 965 – 528 = ___

Answer: 528 – 8 = 520 965 + 8 = 973 973 – 520 = 453 The difference is 453.

Question 28. 384 – 118 = ____

Answer: 684 + 4 = 688 118 – 4 = 114 688 – 114 = 574 The difference is 574.

8.9 Subtract Three-Digit Numbers

Question 29. Estimate: ___ 963 – 51 = ___

Answer: Step 1: Estimate. Round each number to the nearest hundred. 963 = 1000 51 = 100 1000 – 100 = 900 Step 2: Find the difference. Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup. 963 -51 = 912 912 is close to 900. So, the answer is reasonable.

Question 30. Estimate: ___ 878 – 594 = ___

Answer: Step 1: Estimate. Round each number to the nearest hundred. 878 = 900 594 = 600 900 – 600 = 300 Step 2: Find the difference. Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup. 878 – 594 = 284 284 is close to 300. So, the answer is reasonable.

Question 31. Estimate: ___ 766 – 297 = ___

Answer: Step 1: Estimate. Round each number to the nearest hundred. 766 = 800 297 = 300 800 – 300 = 500 Step 2: Find the difference. Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup. 766 – 297 = 469 469 is close to 500. So, the answer is reasonable.

8.10 Relate Addition and Subtraction

Answer: 649 +227 876 Now you have to do the inverse operation of the sum. 876 -227 649

8.11 Problem Solving: Addition and Subtraction

Answer: Given that, There are 532 dogs enrolled in police academies. 246 dogs graduate in July, and 187 dogs graduate in August. 246 + 187 = 433 532 -433 99 Thus 99 dogs are still needed to graduate.

Answer: The numbers round to 300 when rounded to the nearest hundred is 298, 309, 347 Thus the correct answer is the option a, b, c.

Answer: Given, You buy 18 cups of yogurt. The yogurt is sold in packs of 6 cups. 18/6 = 3 packs Thus the correct answer is option c.

Answer: Given, A bedroom floor is 9 feet long and 8 feet wide. The area of the rectangle = l × w A = 9ft × 8ft A = 72 sq. ft Thus the area of the bedroom floor is 72 sq. ft.

Answer: Your friend says 458 – 298 = 160. Your friend is correct. The correct answer is option a.

Answer: Your friend says she needs (9 × 3) + (3 × 9) = 27 × 27 = 54 tiles to make the design. Her thinking is incorrect because she needs to add 27 and 27 but she multiplied. (9 × 3) + (3 × 9) = 27 + 27 = 54

Answer: Given, Your friend says the greatest number he can make with the digits 7, 9, and 8 using each digit only once is 879 Your friend is incorrect because the greatest number with the digits 7, 9, and 8 is 987.

Answer: The count starts from 0. The count jumps from 0 and skips for every 3s. 3 × 7 = 21 Thus the correct answer is option c.

Answer: 548 +372 920

Answer: According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. Options A and D show the equation for the Associative Property of Addition.

Answer: Given, A teacher takes 7 students on a field trip. Each student pays$5. 7 × $5 = $35 Thus the teacher collects $35 in all. The correct answer is option c.

Answer: You can divide the figure into two parts. Figure 1: l = 4m b = 3m A = l × b A = 4 × 3 = 12 sq. m Figure 2: l = 8m b = 3m A = l × b A = 8 × 3 = 24 sq. m Add the area of both the figures 12 + 24 = 36 sq.m Thus the correct answer is option D.

Answer: Given that, There are 459 girls and 552 boys in school. Subtract the number of girls from the number of boys. 552 -459 93 Thus the correct answer is option b.

Answer: 1, 3, 9, 27 are the multiples of 3. Thus the correct answer is option c.

Answer: Given that, A smoothie shop sells 368 smoothies in July and 205 smoothies in August. 368 -205 163 Thus the shop sell 163 smoothies in July than in August.

Answer: There are 16 counters in the first figure 2 × 8 = 16 There are 16 counters in the second figure 4 × 4 = 16 There are 15 counters in the third figure 5 × 3 = 15 Thus the correct answer is option c.

Complete the table

Answer: You can find the area of classroom A by using the composite figure. The shape of classroom A is square. a = 10 yd Area of the classroom is a × a A = 10 × 10 = 100 sq.yd Thus the area of the classroom A is 100 sq. yd Another way: l = 10 yd w = 3 yd A = 10 × 3 = 30 sq. yd l = 10 yd A = 8 × 4 = 32 sq. yd l = 10 yd w = 3 yd A = 10 × 3 = 30 sq. yd

b. Find the total area of all of the classrooms in square yards.

Answer: Area of the classroom is a × a A = 10 × 10 = 100 sq.yd Thus the area of the classroom A is 100 sq. yd Area of Classroom D = 10 × 7 = 70 sq.yd Area of Classroom B = 11 × 7 = 77 sq.yd Area of Classroom C = 12 × 7 = 84 sq. yd, 8 × 3 = 24 sq.yd Area of Classroom C = 84 + 24 = 108 sq. yd Total area of the classrooms = 100 + 70 + 77 + 108 = 355 sq. yd

c. Estimate the number of rolls of carpet needed for the classrooms. Explain.

Answer: There are 4 classrooms. So, the estimated number of rolls of carpet is 4.

d. Find the area of the hallway in square yards. Is there enough carpet for the hallway?

Answer: Let the number of students in your class is 47. By this, we can estimate the total number of students in your grade i.e., 50. The total number of students in your grade is 50.

c. How does your estimate compare to the actual number of students in your grade? Explain.

Answer: You can compare the number of students in the above table with the actual number of students in your grade.

d. What is the total number of students in your school?

Answer: Add the number of students of all the grades 40+ 50 + 52 + 47 + 47 + 50 = 286 Thus there are 286 students in your school.

e. Write and answer a question using the information from the table above.

Answer: Compare the number of students in grade 3 with the actual number of students in your school in grade 3? The estimated number of students in grade 3 in the above table is 50. The actual number of students in your school is 48. 50 – 48 = 2

f. What is one reason your principal may want to know the total number of students in your class, grade, or school?

Answer: Shaping a vision of academic success for all students.

Conclusion:

I wish the information provided in this BIM Answers Grade 3 Chapter 8 Add and Subtract Multi-Digit Numbers pdf is helpful for you. This pdf helps you to score the highest marks in the exams. Get the answers of Bigideas Math Grade 3 Chapter 8 Add and Subtract Multi-Digit Numbers from here. Follow our page to get the solutions with a brief explanation for all the 3rd-grade chapters from 1 to 15.

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Go Math Grade 4 Chapter 2 Answer Key Pdf Multiply by 1-Digit Numbers

Go Math Grade 4 Chapter 2 Answer Key Pdf: contains 4th Standard Go Math solutions which help the students to score well in the exams. This Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers will make students understand the concepts easily. In this, each and every question was explained intimately . And the answers in this chapter are explained in a simple way that anyone can understand easily.

Multiply by 1-Digit Numbers Go Math Grade 4 Chapter 2 Answer Key Pdf

This chapter 2 contains Multiplication Comparisons, Multiplying using Distributive property and Expanded form, Estimate products, etc are explained clearly which makes the scholars learn quickly. Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers . questions are explained in a basic way that students will never feel any difficulty in learning. By this, students can gain good knowledge and this is helpful in finish student’s assignments also.

Lesson 1: Algebra • Multiplication Comparisons

Common Core – Multiplication Comparisons – Page No. 67

• Common Core – Multiplication Comparisons – Lesson Check – Page No. 68

Multiplication Comparisons – Page No. 71

Lesson 2: Algebra • Comparison Problems

• Common Core – Comparison Problems – Page No. 73

Common Core – Comparison Problems – Lesson Check – Page No. 74

Comparison problems – page no. 77, comparison problems – page no. 78.

Lesson 3: Multiply Tens, Hundreds, and Thousands

• Common Core – Multiply Tens, Hundreds, and Thousands – Page No. 79

Common Core – Multiply Tens, Hundreds, and Thousands – Lesson Check – Page No. 80

Multiply tens, hundreds, and thousands – page no. 83, multiply tens, hundreds, and thousands – page no. 84.

Lesson 4: Estimate Products

• Common Core – Estimate Products – Page No. 85

Common Core – Estimate Products – Lesson Check – Page No. 86

Estimate products – page no. 89, estimate products – page no. 90.

Lesson 5: Investigate • Multiply Using the Distributive Property

• Common Core – Multiply Using the Distributive Property – Page No. 91

Common Core – Multiply Using the Distributive Property – Lesson Check – Page No. 92

Multiply using the distributive property – page no. 95, multiply using the distributive property – page no. 96.

Lesson 6: Multiply Using Expanded Form

• Common Core – Multiply Using Expanded Form – Page No. 97
• Common Core – Multiply Using Expanded Form – Lesson Check – Page No. 98

Multiply Using Expanded Form – Page No. 101

Multiply using expanded form – page no. 102.

Lesson 7: Multiply Using Partial Products

• Common Core – Multiply Using Partial Products – Page No. 103
• Common Core – Multiply Using Partial Products – Lesson Check – Page No. 104

Multiply Using Partial Products – Page No. 105

Multiply using partial products – page no. 106, multiply using partial products – page no. 109, multiply using partial products – page no. 110.

Lesson 8: Multiply Using Mental Math

• Common Core – Multiply Using Mental Math – Page No. 111

Common Core – Multiply Using Mental Math – Lesson Check – Page No. 112

Multiply using mental math – page no. 115, multiply using mental math – page no. 116.

Lesson 9: Problem Solving • Multistep Multiplication Problems

• Common Core – Problem Solving Multistep Multiplication Problems – Page No. 117

Common Core – Problem Solving Multistep Multiplication Problems – Lesson Check – Page No. 118

Problem solving multistep multiplication problems – page no. 121.

Lesson 10: Multiply 2-Digit Numbers with Regrouping

Common Core – Multiply 2-Digit Numbers with Regrouping – Page No. 123

Common core – multiply 2-digit numbers with regrouping – lesson check – page no. 124, multiply 2-digit numbers with regrouping – page no. 127, multiply 2-digit numbers with regrouping – page no. 128.

Lesson 11: Multiply 3-Digit and 4-Digit Numbers with Regrouping

• Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 129

Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Lesson Check – Page No. 130

Lesson 12: Algebra • Solve Multistep Problems Using Equations

Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 133

Multiply 3-digit and 4-digit numbers with regrouping – page no. 134.

• Common Core – Solve Multistep Problems Using Equations – Page No. 135

Common Core – Solve Multistep Problems Using Equations – Lesson Check – Page No. 136

Chapter 2 Review/Test

Review/Test – Page No. 137

Review/test – page no. 138, review/test – page no. 139, review/test – page no. 140, review/test – page no. 141, review/test – page no. 142, page no. 147, page no. 148.

Write a comparison sentence.

Question 1. 6 × 3 = 18 6 times as many as 3 is 18 .

Question 2. 63 = 7 × 9

Answer: 63 is 7 times as many as 9.

Question 3. 5 × 4 = 20

Answer: 5 times as many as 4 is 20.

Explanation:

Question 4. 48 = 8 × 6

Answer: 48 is 6 times as many as 8.

Write an equation.

Question 5. 2 times as many as 8 is 16.

Answer: 2 × 8 = 16

Go Math Grade 4 Answer Key Chapter 2 Question 6. 42 is 6 times as many as 7.

Answer: 42 = 6 × 7

Question 7. 3 times as many as 5 is 15.

Answer: 3 × 5 = 15

Question 8. 36 is 9 times as many as 4. Answer: 36 = 9 × 4

Question 9. 72 is 8 times as many as 9. Answer: 72 = 8 × 9

Question 10. 5 times as many as 6 is 30. Answer: 5 × 6 = 30

Problem Solving

Question 11. Alan is 14 years old. This is twice as old as his brother James is. How old is James?

Answer: 7 years old.

Explanation: Alan’s age is 14 years old and his brother is James is twice younger than Alan, So James’s age is 14÷2= 7.

Question 12. There are 27 campers. This is nine times as many as the number of counselors. How many counselors are there?

Answer: 3 counselors.

Explanation: 27 campers= 9× no.of counselors, So no.of counselors are 27÷9= 3.

Question 13.

Draw a model, and write an equation to represent “4 times as many as 3 is 12.” Explain your work.

Answer: 4×3= 12.

Common Core – Multiplication Comparisons – Lesson Check – Page No. 68

Question 1. Which equation best represents the comparison sentence? 24 is 4 times as many as 6. Options: a. 24 × 4 = 6 b. 24 = 4 × 6 c. 24 = 4 + 6 d. 4 + 6 = 24

Question 2. Which comparison sentence best represents the equation? 5 × 9 = 45 Options: a. 5 more than 9 is 45. b. 9 is 5 times as many as 45. c. 5 is 9 times as many as 45. d. 45 is 5 times as many as 9.

Spiral Review

Question 3. Which of the following statements correctly compares the numbers? Options: a. 273,915 > 274,951 b. 134,605 < 143,605 c. 529,058 > 530,037 d. 452,731 > 452,819

Explanation: 134,605 is lesser compared to 143,605.

Question 4. What is the standard form for 200,000 + 80,000 + 700 + 6? Options: a. 2,876 b. 28,706 c. 208,706 d. 280,706

Explanation: 200,000+80,000+700+6= 280,706.

Go Math Grade 4 Chapter 2 Answer Key Pdf Question 5. Sean and Leah are playing a computer game. Sean scored 72,491 points. Leah scored 19,326 points more than Sean. How many points did Leah score? Options: a. 53,615 b. 91,717 c. 91,815 d. 91,817

Explanation: Sean’s score is 72,491 and Leah’s score is 19,326 more than Sean’s score. So Sean’s score is 72,491+19,326 = 91,817.

Question 6. A baseball stadium has 38,496 seats. Rounded to the nearest thousand, how many seats is this? Options: a. 38,000 b. 38,500 c. 39,000 d. 40,000

Explanation: Round off to the nearest thousand is 38,000.

Draw a model. Write an equation and solve.

Question 2. Last month Kim trained 3 times as many dogs as cats. If the total number of cats and dogs she trained last month is 28, how many cats did Kim train?

Explanation: Let the cats trained to be X and dogs trained to be 3X. Total Cats and Dogs she trained are 28, then X+3X= 28 and X= 7. Therefore Cats trained are 7.

Question 3. How many more dogs than cats did Kim train?

Answer: 21 dogs

Explanation: 3×7= 21.

Practice: Copy and Solve Draw a model. Write an equation and solve.

Question 4. At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs, how many dogs are spaniels?

Answer: 24.

Explanation: Let spaniels be S and the boxers be 4S. As the total is 30, S+4S=30 then 5S=30. Therefore S is 6. Spaniels are 6 and boxers are 4 times as many as spaniels. So boxers are 4×6=24.

Question 5. There are 5 times as many yellow labs as terriers in the dog park. If there are a total of 18 dogs, how many dogs are terriers?

Explanation: Let the Terriers be T and yellow labs be 5T. As total dogs are 18, 5T+T=18, and therefore T=18/6 which is 3. Terriers are 3.

Question 6. Ben has 3 times as many guppies as goldfish. If he has a total of 20 fish, how many guppies does he have?

Answer: 15.

Explanation: Let Goldfish be X and Guppies be 3X, So X+3X= 20. Therefore X= 5. So guppies are 3×5= 15.

Question 7. Carlita saw 5 times as many robins as cardinals while bird watching. She saw a total of 24 birds. How many more robins did she see than cardinals?

Answer: 4 cardinals and 20 robins.

Explanation: Let the cardinals be X and robins be 5X. Then the total is 5X+X=24 then X= 4. So Carlita saw 4 cardinals and 5×4= 20 robins.

Multiplication Comparisons – Page No. 72

Answer: Cliff diagram is correct.

Explanation: Mr. Luna’s travels east and west are irrelevant to the question. As he drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.

Question 9. Use Reasoning Valerie and Bret have a total of 24 dog show ribbons. Bret has twice as many ribbons as Valerie. How many ribbons does each have? Valerie’s ribbons: ______          Bret’s ribbons: ______

Answer: Valerie has 8 and Bret has 16.

Explanation: Let the Valerie ribbons be X and Bret’s ribbons be 2X and the total be X+2X= 24. Therefore X= 8. Valerie has 8 and Bret has 2×8= 16.

Question 10. Noah built a fenced dog run that is 8 yards long and 6 yards wide. He placed posts at every corner and every yard along the length and width of the run. How many posts did he use?

Answer: 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Explanation: As there are 7 posts along one 8 yard side and 5 posts along one 6 yard side, so he used 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Common Core – Comparison Problems – Page No. 73

Go Math Grade 4 Lesson 2.2 Answer Key Question 2. At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there? ______ monkeys

Answer: 18 monkeys.

Question 3. Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?

Answer: 49 inches.

Question 4. Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?

Question 5. Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?

Answer: 36 white cars.

Explanation: Let yellow cars be X, As white cars are 9 times as many as yellow cars, So white cars be 9X. Therefore 9X+X=40, X=4. So no.of white cars are 9×4= 36.

Question 6. Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many more points did she score in the second game?

Answer: 30 points.

Explanation: Let the first game points be X and the second game points be 6X. Sue’s total score is 35 points in two games so 6X+X= 35 then X is 5. Therefore the second game score is 6×5= 30.

Algebra Multiplication Comparisons Lesson 2.2 Reteach Question 7. Write a problem involving how much more than and solve it. Explain how drawing a diagram helped you solve the problem.

Answer: Mike has 10 chocolates and John has 5 chocolates. How many more chocolates does Chirs have? 5 chocolates more Chirs have.

Question 1. Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have? Options: a. 7 b. 14 c. 18 d. 21

Explanation: Let the X be pencil erasers of Sam and Sari erasers be 3X. As Sari and Sam together have 28 erasers. So 3X+X= 28. And X is 7. Then Sari has 3×7= 21.

Question 2. In Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies? Options: a. 5 b. 12 c. 15 d. 18

Explanation: Let Guppies be X and Goldfishes be 6X. And the total fishes are 21, So X+6X= 21 then X= 3. So Goldfishes are 6×3= 18.

Question 3. Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have? Options: a. 3 b. 12 c. 24 d. 27

Explanation: Barbara has 9 stuffed animals and Trish has 3 times as Barbara, So 9×3= 27.

4th Grade Go Math Pdf Chapter 2 Lesson 2 Answer Key Question 4. There are 104 students in the fourth grade at Allison’s school. One day, 15 fourth-graders were absent. How many fourth-graders were at school that day? Options: a. 89 b. 91 c. 99 d. 119

Explanation: Total number of students in fourth grade is 104, as 15 students were absent 104-15= 89.

Question 5. Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks. What is the correct order of the boys from the least to the greatest number of rocks owned? Options: a. Jose, Albert, Joshua b. Jose, Joshua, Albert c. Albert, Jose, Joshua d. Joshua, Albert, Jose

Explanation: As 98<107<112. So Jose, Albert, Joshua.

Question 6. Alicia has 32 stickers. This is 4 times as many stickers as Benita has. How many stickers does Benita have? Options: a. 6 b. 8 c. 9 d. 28

Explanation: Let Benita stickers be S and Alicia has 32 stickers, So 4×S= 32. Therefore Benita stickers are 8.

Answer: 2×= 1000.

Explanation: 2×500 is 2 times 5 hundreds, which is equal to 10 hundreds and 10 hundreds are equal to 1000.

Complete the pattern.

Question 2. 3 × 8 = 2 i. 3 × 80 = _____ ii. 3 × 800 = _____ iii. 3 × 8,000 = _____

Answer: 240, 2400, 24,000.

Explanation: 3×80= 240 3×800= 2400 3×8000= 24,000

Question 3. 6 × 2 = 12 i. 6 × 12 = _____ ii. 6 × 120 = _____ iii. 6 × 1,200 = _____

Answer: 72, 720, 7200.

Explanation: 6×12= 72 6×120= 720 6×1200= 7200.

Question 4. i. 4 × 5 = _____ ii. 4 × 50 = _____ iii. 4 × 500 = _____ iv. 4 × 5,000 = _____

Answer: 20, 200, 2000, 20,000.

Explanation: 4×5= 20 4×50= 200 4×500= 2000 4×5,000= 20,000.

Find the product.

Question 5. 6 × 500 = 6 × _____ hundreds = _____ hundreds = _____

Answer: 6×5 hundreds = 30  hundreds.

Explanation: 6 × 500 = 6 × 5 hundreds = 30 hundreds = 3000

Question 6. 9 × 5,000 = 9 × _____ thousands = _____ thousands = _____

Answer: 9 × 5 thousands = 45 thousands.

Explanation: 9 × 5 thousands = 45 thousands. = 45,000.

Question 7. 7 × 6,000 = _____

Answer: 42,000.

Question 8. 4 × 80 = _____

Answer: 320

Question 9. 3 × 500 = _____

Answer: 1500

Use Reasoning Algebra Find the missing factor.

Question 10. _____ × 9,000 = 63,000

Explanation: As 7×9= 63

Question 11. 7 × _____ = 56,000

Explanation: 7×8= 56.

Question 12. 8 × _____ = 3,200

Explanation: 8×4= 32.

Question 13. Communicate How does the number of zeros in the product of 8 and 5,000 compare to the number of zeros in the factors? Explain.

Answer: 8×5=40.

Explanation: There are 4 zeros in the product and 3 zeros only in the factors. Because there is a zero in basic fact as 8×5=40.

Question 14. Joe’s Fun and Sun rents beach chairs. The store rented 300 beach chairs each month in April and in May. The store rented 600 beach chairs each month from June through September. How many beach chairs did the store rent during the 6 months? a. What do you need to know?

Answer: We need to know about the total number of beach chairs rented during the 6 months.

Question 14. b. How will you find the number of beach chairs?

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000

Explanation: We will multiply 2 times 300 and 4 times 600 and the will add the product.

Question 14. c. Show the steps you use to solve the problem.

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Question 14. d. Complete the sentences. For April and May, a total of ______ beach chairs were rented.

Answer: 600

Explanation: As the store rented 300 beach chairs in April and May, So 300×2= 600.

Question 14. For June through September, a total of _____ beach chairs were rented.

Answer: 2400

Explanation: As the store rented 600 beach chairs from June to September, So 600×4= 2400.

Question 14. Joe’s Fun and Sun rented _____ beach chairs during the 6 months.

Answer: 3,000

Explanation: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Go Math Grade 4 Chapter 2 Extra Practice Answer Key Question 15. Mariah makes bead necklaces. Beads are packaged in bags of 50 and bags of 200. Mariah bought 4 bags of 50 beads and 3 bags of 200 beads. How many beads did Mariah buy?

Answer: 800 beads.

Explanation: Mariah bought 4 bags of 50 beads which is 4×50= 200 beads. And 3 bags of 200 beads which is 3×200= 600. Total beads Mariah bought are 200+600= 800.

Answer: 3, 5, 110

Explanation: 3×20+5×10= 110.

Common Core – Multiply Tens, Hundreds, and Thousands – Page No. 79

Question 1. 4 × 7,000 = 28,000 Think: 4 × 7 = 28 So, 4 × 7,000 = 28,000

Question 2. 9 × 60 = _____

Answer: 540

Explanation: 9×6= 54.

Question 3. 8 × 200 = _____

Answer: 1600

Explanation: 8×2=16

Question 4. 5 × 6,000 = _____

Answer: 30,000.

Explanation: 5×6=30.

Question 5. 7 × 800 = _____

Answer: 5600

Question 6. 8 × 90 = _____

Answer: 720

Explanation: 8×9=72.

Question 7. 6 × 3,000 = _____

Answer: 18,000.

Explanation: 6×3= 18.

Question 8. 3 × 8,000 = _____

Answer: 24,000

Explanation: 3×8= 24.

Question 9. 5 × 500 = _____

Answer: 2500.

Explanation: 5×5= 25.

Question 10. 9 × 4,000 = _____

Answer: 36,000

Explanation: 9×4= 36.

Go Math Grade 4 Chapter 2 Pdf Question 11. 7 × 7,000 = _____

Answer: 49,000.

Explanation: 7×7= 49.

Question 12. 3 × 40 = _____

Answer: 120.

Explanation: 3×4= 12.

Question 13. 4 × 5,000 = _____

Answer: 20,000.

Explanation: 4×5= 20.

Question 14. 2 × 9,000 = _____

Answer: 18,000

Explanation: 2×9= 18.

Question 15. A bank teller has 7 rolls of coins. Each roll has 40 coins. How many coins does the bank teller have?

Answer: 280 coins.

Explanation: Bank teller has 7 rolls of coins. As each roll has 40 coins, So total coins are 7×40= 280

Question 16. Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy?

Answer: 2,500.

Explanation: Total number of sheets of papers in each package are 500, And Theo buys 5 packages of papers. So total sheets of paper Theo bought are 500×5= 2,500.

Question 1. A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours? Options: a. 200 miles b. 2,000 miles c. 20,000 miles d. 200,000 miles

Explanation: The speed of the plane is 400 miles per hour. In 5 hours plane can travel 400×5= 2,000 miles.

Question 2. One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all? Options: a. 2,000 b. 12,000 c. 120,000 d. 200,000

Explanation: Shirts made in one week are 2000 in 6 different colors. So total shirts made in all are 2000×6= 12,000.

Question 3. Which comparison sentence best represents the equation? 6 × 7 = 42 Options: a. 7 is 6 times as many as 42. b. 6 is 7 times as many as 42. c. 42 is 6 times as many as 7. d. 6 more than 7 is 42.

Explanation: By comparing 42= 6×7 represents the equation.

Question 4. The population of Middleton is six thousand, fifty-four people. Which of the following shows this number written in standard form? Options: a. 654 b. 6,054 c. 6,504 d. 6,540

Explanation: Six thousand fifty-four is equal to 6,054.

Question 5. In an election for mayor, 85,034 people voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election? Options: a. 17,082 b. 17,182 c. 22,922 d. 152,986

Explanation: Total votes Carl Green has got are 85,034and Maria Lewis got are 67,952. By 85,034-67,952= 17,082 votes Carl Green won the election.

Question 6. Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick? Options: a. 4 b. 5 c. 16 d. 24

Explanation: Let the red peppers be X and green peppers be 4X, And the total she picked is 20 peppers. So X+4X=20, Then X=4. Green peppers she picked are 4×4= 16.

Question 1. Estimate the product by rounding. 5 × 2,213 _____ × _____ = _____

Answer: 5×2000= 10,000

Explanation: The rounding off for 2,213 is 2000. So 5×2000= 10,000.

Question 2. Estimate the product by finding two numbers the exact answer is between. 5 × 2,213

Answer: 5×2000= 10,000 and 5×3000= 15,000.

Explanation: The rounding off for 2,213 is 2000 and 3000. So 5×2000= 10,000 and 5×3000= 15,000.

Tell whether the exact answer is reasonable.

Question 3. Kira needs to make color copies of a horse show flyer. The printer can make 24 copies in 1 minute. Kira says the printer makes 114 copies in 6 minutes.

Answer: Kira is incorrect.

Explanation: As the printer can make 24 copies in 1 minute, So if we take 24 rounds off to 20 or 30 then the printer makes 120 or 180 copies. So Kira is incorrect.

Question 4. Jones Elementary is having a car wash to raise money for a community horse trail. Each car wash ticket costs $8. Tiara says the school will receive $1,000 if 125 tickets are sold.

Answer: Tiara says correct.

Explanation: As 1000÷125= 8 which is each car wash ticket cost. So the answer is reasonable.

Question 5. Evaluate Reasonableness Mrs. Hense sells a roll of coastal Bermuda horse hay for $58. She says she will make $174 if she sells 3 rolls.

Answer: The answer is reasonable.

Explanation: As 174 is the nearest rounding off to 180. So the answer is reasonable.

Question 6. Mr. Brown sells horse supplies. A pair of riding gloves sells for $16. He says he will make $144 if he sells 9 pairs.

Answer: The answer is reasonable

Explanation: As 144 is between 90 and 180, So the answer is reasonable. Here we will take rounding off for 9 as 10 and 20. So the answer must be between 90 and 180.

Question 7. Path A and Path B are walking paths used for horses. Path A is 118 feet long. Path B is 180 feet long. Carlos walks his horse down each path 3 times. Which path did Carlos use to walk his horse about 500 feet? Explain.

Answer: Path B

Explanation: 118 is rounded off to 100 and then multiply with 3, 100  Then round off 180 to 200 and multiply with 3, 200  As 500 is closer to estimate of 600 compared to 300. So Path B is correct.

Answer: 600 and 900.

Explanation: 1let 265 be rounded off 200 and 300. As fourth-grade students sell 3 times as many as third-grade students, So 200 and 300  So tickets sold between 600 and 900.

Predict whether the exact answer will be less than or greater than the estimate. Explain your answer.

Question 9. The food stand at the zoo sold 2,514 pounds of hamburger last month. The average cost of a pound of hamburger is $2. Jeremy estimates that about $6,000 worth of hamburger was sold last month.

Answer: Lesser than the actual amount of hamburger.

Explanation: As the amount of hamburger sold is 468 pounds less than the estimated amount of 3000 pounds. So, the answer will be less than estimated.

Question 10. A zoo bought 2,240 pounds of fresh food for the bears this month. The average cost of a pound of food is $4. Jeremy estimates that about $8,000 was spent on fresh food for the bears this month.

Answer: Greater than the actual amount of food bought.

Explanation: As the actual amount of food bought for the bears this month was 240 pounds greater than the estimated amount of 2,000 pounds. So, the answer will be greater than the estimated amount.

Common Core – Estimate Products – Page No. 85

Estimate the product by rounding.

Question 1. 4 × 472 4 × 472 ↓ 4 × 500 = 2,000

Question 2. 2 × 6,254

Answer: 12,000.

Explanation: The nearest rounding off for 6,254 is 6,000. So 2×6,000= 12,000.

Question 3. 9 × 54

Answer: 450

Explanation: The nearest rounding off for 54 is 50. So 9×50= 450.

Question 4. 5 × 5,503

Explanation: The nearest rounding off for 5,503 is 6,000. So 5×6,000= 30,000.

Question 5. 3 × 832

Answer: 2,400.

Explanation: The nearest rounding off for 832 is 800. So 3×800= 2,400.

Question 6. 6 × 98

Answer: The nearest rounding off for 98 is 100. So 6×100= 600.

Go Math Grade 4 Estimate Products Lesson 2.4 Question 7. 8 × 3,250

Answer: The nearest rounding off for 3,250 is 3,000. So 8×3,000= 24,000.

Question 8. 7 × 777

Answer: 5,600.

Explanation: The nearest rounding off for 777 is 800. So 7×800= 5,600.

Find two numbers the exact answer is between.

Question 9. 3 × 567

Answer: 1500 and 1800.

Explanation: The rounding off for 567 is 500 and 600. So 3×500= 1500 and 3×600= 1800.

Question 10. 6 × 7,381

Answer: 42,000 and 48,000.

Explanation: The rounding off for 7,381 is 7,000 and 8,000. So 6×7000= 42,000 and 6×8000= 48,000.

Question 11. 4 × 94

Answer: 360 and 400.

Explanation: The rounding off for 94 is 90 and 100. So 4×90= 360 and 4×100= 400.

Question 12. 6 × 684

Answer: 3600 and 4200

Explanation: The rounding off for 684 is 600 and 700. So 6×600= 3600 and 6×700= 4200.

Question 13. Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable? Explain

Answer: Yes.

Explanation: As the round-off for 365 can be 300 or 400. So 8×300= 2,400 and 8×400= 3,200. The estimated answer can be between 2,400 to 3,200. So the answer is Yes.

Question 14. Most Americans throw away about 1,365 pounds of trash each year. Is it reasonable to estimate that Americans throw away over 10,000 pounds of trash in 5 years? Explain.

Answer: No.

Explanation: As the round-off for 1,365 can be 1000 or 2000. So 5×1000= 5,000 and 5×2000= 10,000. The estimated answer can be between 5,000 to 10,000.

Question 1. A theater has 4,650 seats. If the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all? Options: a. 2,500 b. 10,000 c. 25,000 d. 30,000

Explanation: As the nearest round off for 4,650 is 5,000. So 5,000×5= 25,000.

Question 2. Washington Elementary has 4,358 students. Jefferson High School has 3 times as many students as Washington Elementary. About how many students does Jefferson High School have? Options: a. 16,000 b. 12,000 c. 10,000 d. 1,200

Explanation: As the nearest round off for 4,358 is 4,000. So 4,000×3= 12,000.

Question 3. Diego has 4 times as many autographed baseballs as Melanie has. Diego has 24 autographed baseballs. How many autographed baseballs does Melanie have? Options: a. 28 b. 20 c. 8 d. 6

Explanation: Let the Melanie baseballs be S. As Diego has 4 times as many as Melanie and Diego has a total of 24 baseballs. So 4×S= 24, Then S= 24÷4 which is 6.

Go Math Grade 4 Lesson 2.4 Estimate Products Question 4. Mr. Turkowski bought 4 boxes of envelopes at the office supply store. Each box has 500 envelopes. How many envelopes did Mr. Turkowski buy? Options: a. 200 b. 504 c. 2,000 d. 20,000

Explanation: Turkowski has 4 boxes of envelopes and each box contains 500 envelopes, So total envelopes did Turkowski bought are 4×500= 2,000.

Question 5. Pennsylvania has a land area of 44,816 square miles. Which of the following shows the land area of Pennsylvania rounded to the nearest hundred? Options: a. 44,000 square miles b. 44,800 square miles c. 44,900 square miles d. 45,000 square miles

Explanation: As the nearest round off for 44,816 is 44,800.

Explanation: Comedy and action movies that are rented in last year are 6,720+5,540= 12,260.

Model the product on the grid. Record the product.

Explanation: 3×13= 3 ×(10+3) =(3×10)+ (3×3) =30+9 =39

Answer: 70.

Explanation: 6×14= 6×(10+4) = (6×10)+(6×4) = 60+24 = 84

Explanation: 5 × 18 =5 ×(10+8) = (5 × 10)+ (5 ×8) = 50+40 = 90.

Explanation: 4 × 16= (4 × 10)+( 4 ×6) = 40+24 = 64.

Use grid paper or base-ten blocks to model the product. Then record the product.

Question 6. 7 × 12 = ______

Explanation: 7×12 = 7×(10+2) =(7×10)+(7×2) =70+14 84

Question 7. 5 × 16 = ______

Explanation: 5×16= 5×(10+6) =(5×10)+(5×6) = 50+30 = 80

Question 8. 9 × 13 = ______

Answer: 117

Explanation: 9 × 13 = 9 ×(10+3) =(9×10)+(9×3) =90+27 =117

Question 9. Explain how modeling partial products can be used to find the products of greater numbers.

Answer: 25 3= (20+5) 3 =(20×3)+(5×3)= 60+15=75

Explanation: Multiplication is easy. For example, if we take 25 3= (20+5) 3 =(20×3)+(5×3)= 60+15=75

Question 10. Use the Distributive Property to model the product on the grid. Record the product. 4 × 14 = _____

Answer: 56.

Explanation: 4×14= 4×(10+4) =(4×10)+(4×4) =40+16 =56

Answer: A shopkeeper has oranges. He keeps his oranges in the basket having 6 rows and each row has 12 oranges. So how many oranges he owned?

Explanation: From the above picture we can see 6 rows and 12 columns of Oranges. So the total number of Oranges is 6 × 12 = 72 Oranges.

Question 12. Describe how you could change the problem by changing the number of rows of oranges and the number of empty spaces in the picture. Then solve the problem.

Common Core – Multiply Using the Distributive Property – Page No. 91

Answer: 65.

Explanation: 5×10= 50 and 5×3= 15 50+15= 65.

Explanation: 4×10= 40 and 4×4= 16 40+16= 56.

Explanation: 3×10=30 and 3×7= 21 30+21= 51

Explanation: 6×10= 60 and 6×5= 30 60+30= 90

Explanation: As there are 7 columns and 13 rows, So 13×7= 91.

Explanation: As there are 5 columns and 14 rows, So 5×14= 70.

Explanation: As 3×10= 30 and 3×5= 15 30+15= 45.

Explanation: As 5×18 is 90 and 90÷10= 9. So answer is 9.

Question 3. Center City has a population of twenty one thousand, seventy people. Which of the following shows the population written in standard form? Options: a. 21,007 b. 21,070 c. 21,077 d. 21,700

Explanation: Twenty-one thousand seventy is equal to 21,070.

Multiply Using The Distributive Property Lesson 2.5 Answer Key Question 4. Central School collected 12,516 pounds of newspaper to recycle. Eastland School collected 12,615 pounds of newspapers. How many more pounds of newspaper did Eastland School collect than Central School? Options: a. 99 pounds b. 101 pounds c. 199 pounds d. 1,099 pounds

Explanation: Central school has collected 12,516 pounds and Eastland school collected 12,615 pounds. So 12,615-12,516= 99.

Question 5. Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have? Options: a. 20 b. 24 c. 96 d. 100

Explanation: Let Football cards be X and baseball cards be 5X. So 5X+X= 120 in which X= 20. As Allison has 5 times as many baseball cards as football cards. So 5×20= 100.

Question 6. A ruby-throated hummingbird beats its wings about 53 times each second. About how many times does a ruby throated hummingbird beat its wings in 5 seconds? Options: a. 25 b. 58 c. 250 d. 300

Explanation: As the nearest round-off for 53 is 50, So 50×5= 250.

Record the product. Use the expanded form to help.

Question 2. 4 × 59 = _____

Answer: 236

Explanation: 4×(50+9) = (4×50)+(4×9) = 200+36 = 236.

Question 3. 3 × 288 = _____

Answer: 864

Explanation: 3×(200+80+8) = (3×200)+(3×80)+(3×8) = 600+240+24 = 864.

Question 4. 4 × 21 = _____

Explanation: 4×(20+1) = (4×20)+(4×1) = 80+4 = 84.

Question 5. 6 × 35 = _____

Answer: 210

Explanation: 6×(30+5) = (6×30)+(6×5) = 180+30 = 210.

Question 6. A hotel has 128 rooms on each floor. There are 4 floors in all. If 334 of the rooms in the hotel have been cleaned, how many rooms still need to be cleaned?

Answer: 178.

Explanation: The total floors in a hotel are 4 and each floor has 128 rooms, So total rooms in the hotel are 128×4= 512. Of 512 rooms 334 were cleaned and the remaining rooms yet to be cleaned are 512-334= 178.

Question 7. Ben wants to buy 2 blue sweaters for $119 each and 3 brown sweaters for $44 each. How much will Ben spend on the five sweaters?

Answer: $370.

Explanation: Ben wants to buy 2 blue sweaters for $119 each, So 119×2= 238. And 3 brown sweater for $44 each which means 44×3= 132. The total he spent on five sweaters is 238+132= 370.

Question 8. A jeweler has 36 inches of silver chain. She needs 5 times that much to make some necklaces and 3 times that amount to make some bracelets. How much silver chain does the jeweler need to make her necklaces and bracelets?

Answer: 288 inches.

Explanation: As the jeweler has 36 inches of silver chain and she needs 5 times to make some necklaces which means 36×5= 180 and 3 times to make a bracelet which means 36×3= 108. So the total sliver she needs is 180+108= 288.

Question 9. Gretchen walks her dog 3 times a day. Each time she walks the dog, she walks 1,760 yards. How many yards does she walk her dog in 3 days?

Answer: 15,840 yards.

Explanation: Gretchen walks 3 times a day which means for 3 days it will be 9 times. As she walks 1,760 yards, So 1760×9= 15,840.

Question 10. Write an Expression Which expression could you write to show how to multiply 9 × 856 using place value and expanded form?

Answer: (9×800)+(9×50)+(9×6)

Explanation: Place value is the value of each digit in a number. So 856 can be expanded as 800+50+6.

Question 11. Jennifer bought 4 packages of tacks. There are 48 tacks in a package. She used 160 of the tacks to put up posters. How many tacks does she have left? Explain.

Answer: 32.

Explanation: Jennifer bought 4 packages of tacks and each package contains 48 tacks. So total tacks are 48×4= 192. As she used 160 tacks total tacks she left are 192-160= 32

Question 12. What is the total cost of 3 Italian cypress trees?

Answer: $237.

Explanation: The cost of each Italian cypress tree is $79.  The total cost of 3 Italian cypress trees is 79×3= 237.

Go Math Grade 4 Lesson 2.5 Answer Key Homework Question 13. What’s the Error? Tanya says that the difference in the cost of 4 flowering cherry trees and 4 Muskogee crape myrtles is $80. Is she correct? Explain.

Answer: No, Because she used a normal price instead of the discounted price.

Explanation: For 4 and above trees, there is a discount price. So she is wrong.

Question 14. What is the greatest possible product of a 2-digit number and a 1-digit number? Explain how you know.

Answer: 891.

Explanation: The greatest 2 digit number is 99 and the greatest single-digit number is 9. So the product is 99×9= 891.

Answer: (5×300)+(5×80)+(5×1).

Explanation: The expanded form of 381 is 300+80+1.

Common Core – Multiply Using Expanded Form – Page No. 97

Record the product. Use expanded form to help.

Question 1. 7 × 14 = 98 7 × 14 = 7 × (10 + 4) = (7 × 10) + (7 × 4) = 70 + 28 = 98

Question 2. 8 × 43 = _____

Answer: 344.

Explanation: 8×(40+3) = (8×40)+(8×3) = 320+24 = 344.

Question 3. 6 × 532 = _____

Answer: 3,192.

Explanation: 6×(500+30+2) = (6×500)+(6×30)+(6×2) = 3000+180+12 = 3,192.

Question 4. 5 × 923 = _____

Answer: 4,615

Explanation: 5×923= 5×(900+20+3) =(5×900)+(5×20)+(5×3) =4500+100+15 =4,615.

Question 5. 4 × 2,371 = _____

Answer: 9,484

Explanation: 4×2,371= 4×(2000+300+70+1) = (4×2,000)+(4×300)+(4×70)+(4×1) =8000+1200+280+4 =9,484

Question 6. 7 × 1,829 = _____

Answer: 12,803

Explanation: 7×1,829= 7×(1,000+800+20+9) =(7×1,000)+( 7×800)+( 7×20)+( 7×9) =7,000+5600+140+63 =12,803

Question 7. The fourth-grade students at Riverside School are going on a field trip. There are 68 students on each of the 4 buses. How many students are going on the field trip?

Answer: 272 students.

Explanation: No. of buses are 4 and on each bus, there are 68 students. So 68 4= 272.

Question 8. There are 5,280 feet in one mile. Hannah likes to walk 5 miles each week for exercise. How many feet does Hannah walk each week?

Answer: 26,400 feet.

Explanation: There are 5,280 feet in one mile and Hannah walks 5 miles each week, So 5,280 5= 26,400.

Common Core – Multiply Using Expanded Form – Lesson Check – Page No. 98

Question 1. Which expression shows how to multiply 7 × 256 by using expanded form and the Distributive Property? Options: a. (7 × 2) + (7 × 5) + (7 × 6) b. (7 × 200) + (7 × 500) + (7 × 600) c. (7 × 2) + (7 × 50) + (7 × 600) d. (7 × 200) + (7 × 50) + (7 × 6)

Explanation: By Distributive property of multiplication 7×256=(7×200)+(7×50)+(7×6)

Question 2. Sue uses the expression (8 × 3,000) + (8 × 200) + (8 × 9) to help solve a multiplication problem. Which is Sue’s multiplication problem? Options: a. 8 × 329 b. 8 × 3,029 c. 8 × 3,209 d. 8 × 3,290

Explanation: The expression (8×3,000)+(8×200)+(8×9) is written in the Distributive property of multiplication. So 8×3,029.

Question 3. What is another way to write 9 × 200? Options: a. 18 ones b. 18 tens c. 18 hundreds d. 18 thousands

Explanation: 9×200= 1800

Question 4. What is the value of the digit 4 in 46,000? Options: a. 4 ten thousands b. 4 thousands c. 4 hundreds d. 4 tens

Explanation: The place value of 4 in 46,000 is 40,000.

Question 5. Chris bought 6 packages of napkins for his restaurant. There were 200 napkins in each package. How many napkins did Chris buy? Options: a. 120 b. 1,200 c. 12,000 d. 120,000

Explanation: The total packages are 6 and each package contains 200 napkins. So 6 200=1,200.

Lesson 2.6 Multiply Using Expanded Form Question 6. Which of the following lists the numbers in order from least to greatest? Options: a. 8,512; 8,251; 8,125 b. 8,251; 8,125; 8,512 c. 8,125; 8,512; 8,251 d. 8,125; 8,251; 8,512

Explanation: 8,125>8,251>8,512.

Answer: 274.

Explanation: 2×137= 2×(100+30+7) =(2×100)+(2×30)+(2×7) =200+60+14 =274.

Estimate. Then record the product.

Question 2. 1 9 0 ×   3 ———– Estimate: ________ Product: ________

Answer: Estimate: 600 Product: 570.

Explanation: Round off 190 to 200 and 200×3= 600. And the product is 190×3= 570.

Question 3. 4 7 1 ×   4 ———– Estimate: ________ Product: ________

Answer: Estimate: 2000 Product: 1884.

Explanation: Round off 471 to 500 and 500×4= 2000. And the product is 471×4= 1884.

Question 4. 3, 439 ×     7 ———– Estimate: ________ Product: ________

Answer: Estimate: 24,500 Product: 24,073.

Explanation: Round off 3,439 to 3500 and 3500×7= 24,500. And the product is 35000×7= 24,073.

Question 5. $ 5 3 ×   4 ———– Estimate: $ ________ Product: $ ________

Answer: Estimate: $ 240 Product: $ 212

Explanation: Round off 53 to 60 and 60×4= 240. And the product is 53×4= 212.

Go Math 4th Grade Lesson 2.6 Answer Key Question 6. $ 4 7 3 ×      4 ———– Estimate: $ ________ Product: $ ________

Answer: Estimate: $2,000 Product: $1,892.

Explanation: Round off 473 to 500 and 500×4= 2,000. And the product is 473×4= 1892.

Question 7. 6 0 8 ×    6 ———– Estimate: ________ Product: ________

Answer: Estimate: 4,200 Product: 3,648

Explanation: Round off 608 to 700 and 700×6= 4,200. And the product is 608×6= 3,648.

Practice: Copy and Solve Estimate. Then record the product.

Question 8. 2 × 78 = Estimate: ________ Product: ________

Answer: Estimate: 200 Product: 156

Explanation: Round off 78 to 100 and 100×2= 200. And the product is 78×2= 156.

Question 9. 2 × $210 = Estimate: $ ________ Product: $ ________

Answer: Estimate: $600 Product: $420

Explanation: Round off 210 to 300 and 300×2= 600. And the product is 210×2= 420.

Question 10. 2 × $682 = Estimate: $ ________ Product: $ ________

Answer: Estimate: $1,400. Product: $1,364

Explanation: Round off 682 to 700 and 700×2= 1400. And the product is 682×2= 1364.

Question 11. 8 × 8,145 = Estimate: ________ Product: ________

Answer: Estimate: 68,000. Product: 65,160.

Explanation: Round off 8,145 to 8,500 and 8,500×8= 68,000. And the product is 8145×8= 65,160.

Use Reasoning Algebra Find the missing digit.

Question 12. ■5 × 7 ————- 455 ■ = _____

Explanation: 65×7= 455.

Question 13. 2 4 8 ×   3 ————- ■ 44 ■ = _____

Answer: 744

Explanation: 248×3= 744

Question 14. $3 9 5 ×     ■ ———— $2,370 ■ = _____

Explanation: 395×6= 2370

Question 15. 3,748 ×    4 ———- 1 ■,992 ■ = _____

Answer: 14,992

Explanation: 3,748×4= 14,992

Question 16. A store-bought 9 cases of light bulbs in May and 8 cases in June. There are 48 light bulbs in a case. How many light bulbs did the store buy in May and June?

Answer: 816 bulbs.

Explanation: Light bulbs in May are 9 cases and in June are 8 cases. And each case has 48 light bulbs. So 9×48= 432 in May and 8×48= 384 in June. So total light bulbs in May and June are 384+432= 816.

Go Math Chapter 2 Grade 4 Review/Test Answer Key Question 17. Mr. Wilson saved $2,500 to buy airline tickets for his family. He bought 6 airline tickets for $372 each. How much of his savings does Mr. Wilson have after he buys the tickets?

Answer: $268.

Explanation: Mr. Wilson bought 6 tickets and each cost $372, So 372×6= 2,232. The total money Mr. Wilson saved was $2,500. Total Savings are 2500-2232=$268.

Question 18. Coach Ramirez bought 8 cases of bottled water for a road race. There are 24 bottles in each case. After the race, 34 bottles of water were left. How many bottles were used at the race? Explain.

Answer: 158 bottles.

Explanation: Ramirez bought 8 cases of water and each case contains 24 bottles. So the total bottles are 8×24=192 and 34 bottles left. Therefore used bottles are 192-34= 158.

Answer: 1664.

Explanation: The total number of songs in portable media players is 9,000, and Kylie has 832 songs. So Kylie can add 9000-832= 8,168 songs. Lance has 3 times as many songs as Kylie, So Lance has 832×3= 2,496. He can add 9000-2496= 6504 to his player. Therefore 8168-6504=1664 Lance can add 1664 fewer songs to his player than Kylie.

Question 20. James wants to buy the new portable media player shown. He has 5 times as many songs as Susan. Susan has 1,146 songs. Will all of his songs fit on the portable media player? How many songs does James have?

Answer: 5,730 songs. Yes, will fit on the portable media player.

Explanation: Susan has 1,146 songs and James has 5 times as many songs as Susan, So 1,146 5= 5,730 songs will fit on the portable media player.

Question 21. The sum of a 3-digit number and a 1-digit number is 217. The product of the numbers is 642. If one number is between 200 and 225, what are the numbers?

Explanation: As the given product is 642 and the 3 digit number is between 200 and 225, So the 1-digit number is 3 because if we multiply 200 and 225 by 3 we will get the product as 600 and 675 and 642 is in between them. So 642 3= 214. And the one-digit number is 3.

Question 22. Mrs. Jackson bought 6 gallons of juice for a party. Each gallon has 16 cups. After the party, 3 cups of juice were left over. At the party, how many cups did people drink? Show your work and explain how you found your answer.

Answer: 93.

Explanation: Mrs. Jackson bought 6 gallons of juice and each gallon has 16 cups. So total cups of juice is 16 6= 96 cups. And in that 3 cups of juice was left after the party. So 96-3= 93 cups of juice people drank.

Common Core – Multiply Using Partial Products – Page No. 103

Question 1. Estimate: 1,200 2 4 3 ×   6 —————— 1,200 2 4 0 +1 8 —————– 1,458

Question 2. 6 4 0 ×   3 —————— Estimate: _________ Product: _________

Answer: Estimate: 1800 Product: 1920.

Explanation: Rounding off 640 to 600 then the estimated product is 600 3= 1800 and 640 3= 1920. 6 4 0 ×   3 —————— 1800 +120 +0 —————— 1920

Question 3. $ 1 4 9 ×      5 —————— Estimate: $ _________ Product: $ _________

Answer: Estimate: $500 Product: $745

Explanation: Rounding off 149 to 100 the estimated product is 100 5= 500 and 149 5= 745. $ 1 4 9 ×      5 —————— 500 +200 +45 —————— 745

Question 4. 7 2 1 ×   8 —————— Estimate: _________ Product: _________

Answer: Estimate: 5600 Product: 5768

Explanation: Rounding off 721 to 700 the estimated product is 700 8= 5600 and 721 8= 5,768. 7 2 1 ×   8 —————— 5600 +160 +8 —————— 5,768

Practice and Homework Lesson 2.7 Answers 4th Grade Question 5. 2 9 3 ×   4 —————— Estimate: _________ Product: _________

Answer: Estimate: 1,200 Product: 1,172

Explanation: Rounding off 293 to 300 the estimated product is 300 4= 1200 and 293 4=1,172. 2 9 3 ×   4 —————— 800 +360 +12 —————— 1,172

Question 6. $ 4 1 6 ×      6 —————— Estimate: $ _________ Product: $ _________

Answer: Estimate: $2400 Product: $2496

Explanation: Rounding off 293 to 300 then the estimated product is 400 6= 2400 and 416 6= 2496. $ 4 1 6 ×      6 —————— 2400 +60 +36 —————– 2,496

Question 7. 9 6 1 ×    2 —————— Estimate: _________ Product: _________

Answer: Estimate: 2000 Product: 1922

Explanation: Rounding off 961 to 1000 then the estimated product is 1000 2= 2000 and 961 2= 1922. 9 6 1 ×    2 —————— 1800 +120 +2 ——————- 1922

Question 8. 8 3 7 ×   9 —————— Estimate: _________ Product: _________

Answer: Estimate: 7,200 Product: 7,533

Explanation: Rounding off 837 to 800 then the estimated product is 800 9= 7200 and 837 9= 7533.

8 3 7 ×   9 —————— 7200 +270 +63 —————– 7533

Question 9. 6 5 2 ×   4 —————— Estimate: _________ Product: _________

Answer: Estimate: 2,800 Product: 2,608

Explanation: Rounding off 652 to 700 then the estimated product is 700 4= 2800 and 652 4= 2,608. 6 5 2 ×   4 —————— 2400 +200 +8 —————– 2608

Question 10. 3 0 7 ×   3 —————— Estimate: _________ Product: _________

Answer: Estimate: 900 Product: 921

Explanation: Rounding off 307 to 300 then the estimated product is 300 3= 900 and 307 3= 921. 3 0 7 ×   3 ——– 900 +21 —— 921

Question 11. 5 4 3 ×   7 —————— Estimate: _________ Product: _________

Answer: Estimate: 3500 Product: 3,801

Explanation: : Rounding off 543 to 500 then estimated product is 500 7= 3500 and 543 7= 3801. 5 4 3 ×   7 —————— 3500 +280 +21 —————– 3801

Question 12. $ 8 2 2 ×      5 —————— Estimate: $ _________ Product: $ _________

Answer: Estimate: $4,000. Product: $4,110.

Explanation: Explanation: : Rounding off 822 to 800 then estimated product is 800 5= 4000 and 822 5= 4110. $ 8 2 2 ×      5 —————— 4000 +100 +10 —————— 4110

Question 13. A maze at a county fair is made from 275 bales of hay. The maze at the state fair is made from 4 times as many bales of hay. How many bales of hay are used for the maze at the state fair?

Answer: 1100 bales.

Explanation: No. of country fair bales are 275 and state fair bales are 4 times as many as country fair bales. So 275 4= 1100

Go Math Lesson 2.8 4th Grade Answer Key Question 14. Pedro gets 8 hours of sleep each night. How many hours does Pedro sleep in a year with 365 days?

Answer: 2,920 hours.

Explanation: Pedro sleeps 8 hours each night and 365 days Pedro sleeps 365 8= 2,920 hours.

Common Core – Multiply Using Partial Products – Lesson Check – Page No. 104

Question 1. A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours? Options: a. 2,092 miles b. 2,112 miles c. 2,192 miles d. 2,480 miles

Explanation: Average speed of passenger jet is 548 miles per hour. And the plane travels in 4 hours is 548 4= 2,192 miles.

Explanation: By distributive property of multiplication 3 x 157= 3 x(100+50+7) =(3 x100)+(3×50)+(3×7) =300+150+21 =471

Question 3. The school fun fair made $1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales? Options: a. $2,636 b. $2,646 c. $2,736 d. $2,746

Answer: $2746.

Explanation: Money made on games is $1,768 and on food sale is $978. So total money make on games and food sales are 1768+978= 2746.

Explanation: Vermont has 621,760, North Dakota has 646,844 and Alaska has 698,473. So Vermont, North Dakota, Alaska.

Question 5. A National Park covers 218,375 acres. What is this number written in expanded form? Options: a. 200,000 + 10,000 + 8,000 + 300 + 70 + 5 b. 20,000 + 1,000 + 800 + 30 + 75 c. 218 + 375 d. 218 thousand, 375

Explanation: 218,375 is expanded as 200,000 + 10,000 + 8,000 + 300 + 70 + 5

Question 6. Last year a business had profits of $8,000. This year its profits are 5 times as great. What are this year’s profits? Options: a. $4,000 b. $40,000 c. $44,000 d. $400,000

Explanation: Last year’s profit of $8,000 and this year 5 times more. So this year profit is 8000 5= 40,000.

Question 1. To find the product of a two-digit number and a 1-digit number, you can multiply the tens, multiply the ones, and find the sum of each ________________.

Answer: Factor

Explanation: Factors are the numbers which divides the original number completely.

Question 2. The _____________ states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Answer: Distributive Property

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Question 3. 5 × 9 = 45 ______ times as many as ______ is ______ .

Answer: 5 times as many as 9 is 45

Question 4. 24 = 6 × 4 ______ is ______ times as many as ______ .

Answer: 24 is 6 times as many as 4.

Question 5. 54 = 6 × 9 ______ is ______ times as many as ______ .

Answer: 54 is 6 times as many as 9

Question 6. 8 × 6 = 48 ______ times as many as ______ is ______ .

Answer: 48 is 8 times as many as 6.

Question 7. 7 5 × 5 ————— Estimate: ________ Product: ________

Answer: Estimate: 500 Product: 375

Explanation: Rounding off 75 to 100 estimated value is 100×5= 500 and 75×5= 375

Question 8. 1 2 × 6 ————— Estimate: ________ Product: ________

Answer: Estimate: 60 Product: 72

Explanation: Rounding off 12 to 10 estimated value is 10×6= 60 and 12×6= 72

Question 9. 2 8 × 3 —————

Answer: Estimate: 90 Product: 84

Explanation: Rounding off 28 to 30 estimated value is 30×3= 90 and 28×3= 84

Question 10. $4 3 × 6 ————— Estimate: $ ________ Product: $ ________

Answer: Estimate: 300 Product: 258

Explanation: Rounding off 43 to 50 estimated value is 50×6= 300 and 43×6= 258

Question 11. 5 × 64 = _____

Explanation: 5 × 64= 5×(60+4) =(5×60)+(5×4) =300+20 =320

Question 12. 3 × 272 = _____

Answer: 812

Explanation: 3 × 272= 3×(200+70+2) =(3×200)+(3×70)+(3×2) =600+210+6 = 812

Question 13. There are 6 times as many dogs as cats. If the total number of dogs and cats is 21, how many dogs are there?

Answer: 18 dogs.

Explanation: Let cats be X and dogs are as many as 6 so dogs be 6X. As the total number of cats and dogs are X+6X=21, And X= 3 so dogs are 6×3= 18

Answer: 248 Calories.

Explanation: The number of calories of blackberries in one cup are 62 and in 4 cups are 62×4= 248.

Question 15. The skating rink rented 218 pairs of skates during the month of April and 3 times that many in May. How many pairs of skates did the skating rink rent during April and May?

Answer: 872 pairs.

Explanation: No. of pairs of skates in April are 218 and 3 times that many in May. So 3×218= 654. Total skates in April and May are 218+654= 872

Question 1. Break apart the factor 112 to find 7 × 112 by using mental math and addition. 7 × 112 = 7 × (_____ + 12)

Answer: 100

Explanation: 7 × 112 = 7 × (100 + 12) = 7×(100+12) = 700+84 = 784

Find the product. Tell which strategy you used.

Question 2. 4 × 6 × 50 = _____

Answer: 1200, Associative property.

Explanation: 4 × 6 × 50= 4 ×(6×50) =4×(300) =1200.

Question 3. 5 × 420 = _____

Answer: 2100, Use addition

Explanation: 420= 400+20 5×420= 5×(400+20) =(5×400)+(5×20) =2000+100 =2100.

Question 4. 6 × 298 = _____

Answer: 1788, Distributive property.

Explanation: 6×298 = 6×(200+90+8) = (6×200)+( 6×90)+( 6×8) = 1200+540+48 = 1788

Question 5. 14 × 50 = _____

Answer: 700, Halving and doubling.

Explanation: 14×50= (14×25)+(7×50) = 350+350 = 700

Question 6. 32 × 25 = _____

Explanation: 32 × 25= 32× (20+5) =(32×20)+(32×5) =640+160 =800

Question 7. 8 × 25 × 23 = _____

Answer: 4,600, Associative property.

Explanation: 8×25×23=(8×25)× 23 =(200) ×23 4,600

Practice: Copy and Solve Use a strategy to find the product.

Question 8. 16 × 400 = _____

Answer: 6400, Distributive Property.

Explanation: 16×400= (8+8)×400 =(8×400)+ (8×400) =3200+3200 =6400

Question 9. 3 × 31 × 10 = _____

Answer: 930, Associative property.

Explanation: 3×31×10= (3×31)×10 =(93) ×10 =930

Question 10. 3 × 199 = _____

Answer: 597, Distributive property.

Explanation: 3×199=3×(100+90+9) =(3×100)+(3×90)+(3×9) =300+270+27 = 597

Question 11. 3 × 1,021 = _____

Answer: 3063, Distributive Property.

Explanation: 3×1021= 3×(1000+20+1) =(3×1000)+(3×20)+(3×1) =3000+60+3 =3063

Identify Relationships Algebra Use mental math to find the unknown number.

Question 12. 21 × 40 = 840, so 21 × 42 = _____

Answer: 882

Explanation: By Distributive property 21 × 42= 21(40+2) =(21×40)+(21×2) =840+42 =882

Question 13. 9 × 60 = 540, so 18 × 30 = _____

Explanation: As one factor is halved and the other one is doubled and the result is an equivalent expression.

Question 14. The science museum sells dinosaur models to schools and libraries for $107 each. The town library buys 3 models. The town elementary school buys 5 models. What is the total cost of the models the town buys?

Answer: $856.

Explanation: The cost of each dinosaur model is $107, And the town library buys 3 models which cost 107×3= 321, and town elementary school buys 5 models which cost 107×5= 535. Total cost is 321+535= 856.

Question 15. Kyle and Karen each bought 6 books of ride tickets at the fair. Each book has 15 tickets. How many tickets did they buy altogether?

Answer: 180 tickets

Explanation: Kyle and Karen each bought 6 books each that means total of 12 books and each book has 15 tickets. So total tickets both bought are 12×15= 180

Question 16. Three thousand, forty-three people buy tickets at the gate for Section N and one hundred people buy tickets at the gate for Section L. How much money is collected for Section N and Section L at the gate?

Answer: $79575.

Explanation: As 3043 people bought tickets at the gate for Section N, So 3043×25= $76075 and 100 people bought tickets at the gate for Section L, So 100×35= $3500. The total money collected by both sections is 76075+3500= 79575.

Question 17. Use Diagrams Tina and 3 of her friends buy the full season plan for Section M. If there are 45 games in the full season, how much money do they spend?

Answer: $4500.

Explanation: Tina and 3 of her friends which means a total of 4 members bought full season for Section M which costs $25 for each, So total cost is 25×4= 100. If there are 45 games in full seasons then 45×100= $4500.

Question 18. When the full season tickets first went on sale, 2,000 Full Season tickets sold for Section N. Two weeks after the tickets first went on sale, another 1,500 full season tickets were sold for Section N. How much money was spent on full season tickets for Section N in total? How much more money was spent when the tickets first went on sale than after the first two weeks? $ _____ was spent on full season tickets for Section N in total;

Answer: $70,000. $10,000 more

Explanation: The first sale tickets sold are 2,000 for Section N which is 2,000×20= 40,000. And in next sale 1500 tickets sold out which is 1500×20= 30,000. Total money spent are 40,000+30,000= 70,000.

Question 19. Find 6 × 407. Show your work and explain why the strategy you chose works best with the factors.

Answer: 2,442

Explanation: By using Distributive property 6×407= 6×(400+7) =(6×400)+(6×7) =2400+42 =2,442.

Common Core – Multiply Using Mental Math – Page No. 111

Question 1. 6 × 297 Think: 297 = 300 – 3 6 × 297 = 6 × (300 – 3) = (6 × 300) – (6 × 3) = 1,800 – 18 = 1,782; use subtraction

Question 2. 8 × 25 × 23 = _____

Answer: 4,600. Associative property.

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same. 8 × 25 × 23= (8×25)×23 =200×23 =4600

Question 3. 8 × 604 = _____

Answer: 4832, Use Addition.

Explanation: 604= 600+4 8×604= 8×(600+4) =(8×600)+(8×4) =4800+32 =4832.

Question 4. 50 × 28 = _____

Answer: 1400, Halving and doubling.

Explanation: 50×28= (25×28)+(50×14) =700+700 =1400

Question 5. 9 × 199 = _____

Answer: 1,791

Explanation: By Distributive property 9 × 199= 9 ×(100+90+9) =(9×100)+(9×90)+(9×9) =900+810+81 = 1791

Go Math Grade 4 Lesson 2.8 Answer Key Question 6. 20 × 72 × 5 = _____

Answer: 7,200.

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same. 20 × 72 × 5= (20×72) ×5 =1440×5 =7,200.

Question 7. 32 × 25 = _____

Answer: 800.

Explanation: Multiplication. 32×25= 800.

Question 8. Section J in an arena has 20 rows. Each row has 15 seats. All tickets cost $18 each. If all the seats are sold, how much money will the arena collect for Section J?

Answer: $5400.

Explanation: Total rows in the arena are 20 rows and each row has 15 seats. So total seats are 20×15= 300 seats. And each ticket cost is $18, So the total ticket price is 300×15= 5400.

Question 9. At a high school gym, the bleachers are divided into 6 equal sections. Each section can seat 395 people. How many people can be seated in the gym?

Answer: 2,370 people.

Explanation: Total sections are 6 and each section contains 395 people. So total members can be seated in the gym are 395×6= 2,370 people.

Question 1. Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start of school. Each box of pencils cost $2. How much did the school spend on pencils? Options: a. $240 b. $1,200 c. $2,400 d. $4,800

Explanation: Total boxes of pencils are 24 and a school bought 50 cartons of pencils. So total no. of boxes are 24×50=1200 and each box of pencils cost $2. So 1200×2= 2400 school has spent.

Question 2. The school also bought 195 packages of markers. There are 6 markers in a package. How many markers did the school buy? Options: a. 1,170 b. 1,195 c. 1,200 d. 1,230

Explanation: The school bought 195 packages of markers and each package contains 6 markers, So total markers are 195×6= 1170

Question 3. Alex has 175 baseball cards. Rodney has 3 times as many baseball cards as Alex. How many fewer cards does Alex have than Rodney? Options: a. 700 b. 525 c. 450 d. 350

Explanation: Alex has 175 baseball cards and Rodney has 3 times as many as Alex, So total no. of cards Rodney have are 175×3= 525. And Alex has 525-175= 350 fewer cards than Rodney.

Question 4. A theater seats 1,860 people. The last 6 shows have been sold out. Which is the best estimate of the total number of people attending the last 6 shows? Options: a. fewer than 6,000 b. about 6,000 c. fewer than 12,000 d. more than 20,000

Explanation:  No. of seats in a theater are 1,860 people and last 6 shows have been sold out, So 1,860×6= 11,160 which are fewer than 12,000.

Question 5. At one basketball game, there were 1,207 people watching. At the next game, there were 958 people. How many people in all were at the two games? Options: a. 2,155 b. 2,165 c. 2,265 d. 10,787

Explanation: There are 1207 people are watching basketball game and in the next game 958 people are there. So total no. of people are 1,207+958= 2165.

Question 6. Bill bought 4 jigsaw puzzles. Each puzzle has 500 pieces. How many pieces are in all the puzzles altogether? Options: a. 200 b. 900 c. 2,000 d. 20,000

Explanation: Bill bought 4 jigsaw puzzle and each puzzle has 500 pieces. So altogether pieces are 500×4= 2000.

Answer: 112+96= 208.

Explanation: As section A has 8 rows and 14 seats each, So 14×8= 112 and Section B has 6 rows and 16 seats each, So 16×6= 96. Total no. of people are seated in Section A and Section B are 112+96= 208.

Question 1. There are _____________ people seated in Sections A and B for the last show.

Answer: 208.

Explanation: As Section A has 112 people and Section B has 96 people, So 112+96= 208.

Question 2. What if Sections A and B each had 7 rows? How many people would have been seated in Sections A and B?

Explanation: As section A has 7 rows and 14 seats each, So 14×7= 98 and Section B has 7 rows and 16 seats each, So 16×7= 112. Total no. of people are seated in Section A and Section B are 112+98= 210.

Question 3. Brenda’s vegetable garden has 13 rows with 8 plants in each row. Brenda plans to plant peppers in the first 2 rows and the last 2 rows of the garden. The rest of the rows will be tomatoes. How many tomato plants will Brenda plant?

Answer: 72 tomato plants

Explanation: Brenda’s vegetable garden has 13 rows with 8 plants in each row as she plans to plant first 2 rows and last 2 rows with pepper, So 13-4= 9 rows contains tomato plants and each row contains 8 plants, So 9×8= 72 tomato plants.

Question 4. There are 8 rows of 22 chairs set up for an awards ceremony at the school. In each row, the 2 chairs on each end are reserved for students receiving awards. The rest of the chairs are for guests. How many chairs are there for guests?

Answer: 144 Chairs.

Explanation: As there are 8 rows with 22 chairs in each row, So total no. of chairs is 22×8= 176 chairs. As 2 chairs at each end are reserved for students receiving the award, So total chairs reserved are 8×4=32. So remaining chairs are 176-32= 144.

Question 5. Mr. Torres took his students to the dolphin show. Each row in the stadium had 11 seats. One adult sat at each end of a row, and each group of 4 students was seated between 2 adults. Mr. Torres sat by himself. How many adults were there? _____ adults including Mr. Torres

Answer: 13 adults.

Explanation: First we must find total no. of rows, As there are 24 students each group contains 4 students, So 24 4= 6 rows. And one adult sat in each end of the row, So in 6 rows 2 people will sit. Therefore total adults are 6×2=12 adults+ Mr. Torres= 13 adults.

Question 6. Another stadium section has 24 rows of 10 seats each. Describe at least two ways Mrs. Allen’s class can sit if an equal number of students sit in each row.

Answer: 9 rows of 4 students or 6 rows of 6 students.

Explanation: As there are 36 students in Mrs. Allen’s class. So students can sit in 6 rows of 6 students or 9 rows of 4 students.

Question 7. Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 10 inches longer than Ann’s fish. Liz’s fish is 2 inches longer than twice the length of Ann’s fish. Ann’s fish is 12 inches long. Find the length of each toy fish. Carol’s: _____ in.         Liz’s: _____ in.

Answer: Carol’s: 22 in., Liz’s: 26in.

Explanation: Ann’s fish is 12 inches longer and Carol’s fish is 10 inches longer than Ann’s fish which means 10+12= 22 inches, So Carol’s fish is 22 inches. Liz’s fish is 2 inches longer than twice the length of Ann’s fish, which means (2×12) +2=24+2= 26 inches.

Question 8. Evaluate Relationships Nell made a secret code. Each code word has 2 letters. Each word begins with a consonant and ends with a vowel. How many code words can Nell make with 3 consonants and 2 vowels? _____ code words

Answer: 6 ways.

Explanation: As each word begins with a consonant and ends with a vowel, So the first letter can be any one of 3 consonants and the second letter can be either one of 2 vowels. So Nell can make 3×2= 6 ways.

Question 9. Allie is building a patio. The patio will have 8 tiles in each of 13 rows. She has already built the center section with 4 tiles in each of 7 rows. How many more tiles are needed to complete the patio? Show your work.

Answer: 76 tiles.

Explanation: Allie had 8 tiles in each of 13 rows, which means 13×8= 104 tiles. And the center section was built by 4 tiles in each of 7 rows, which means 4×7= 28 tiles. So 104-28= 76 tiles more needed to complete the patio.

Common Core – Problem Solving Multistep Multiplication Problems – Page No. 117

Solve each problem.

Question 2. Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of Jonah’s friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem.

Answer: 375 apples.

Explanation: As Jonah fills 5 baskets which holds 15 apples, So Jonah picked 15×5= 75 apples. And 4 of his friends pick same amount of apples, which means 75×4=300. So total apples Jonah and his friends picked up are 300+75= 375 apples.

Question 3. There are 6 rows of 16 chairs set up for the third-grade play. In the first 4 rows, 2 chairs on each end are reserved for teachers. The rest of the chairs are for students. How many chairs are there for students?

Answer: 80 chairs.

Explanation: As there are 6 rows of 16 chairs which means 16×6= 96 total chairs. And first 4 rows 2 chairs on each end are reserved for teachers, which means 4×4= 16 chairs are reserved for teachers. So 96-16= 80 chairs are left for the students.

Question 1. At a tree farm, there are 9 rows of 36 spruce trees. In each row, 14 of the spruce trees are blue spruce. How many spruce trees are NOT blue spruce? Options: a. 126 b. 198 c. 310 d. 324

Explanation: There are 9 rows of 36 spruce trees which means 9×36= 324 spruce trees. And in that, each row has 14 blue spruce trees which mean 14×9= 126. So 324-126= 198 spruce trees are not blue.

Question 2. Ron is tiling a countertop. He needs to place 54 square tiles in each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. How many white tiles will Ron need? Options: a. 464 b. 432 c. 400 d. 32

Explanation: Ron places 54 square tiles in each of 8 rows which means 54×8=432 tiles. And he randomly places 8 groups of 4 blue tiles which means 8×4= 32 blue tiles are placed. So no. of white tiles are 432-32= 400.

Question 3. Juan reads a book with 368 pages. Savannah reads a book with 172 fewer pages than Juan’s book. How many pages are in the book Savannah reads? Options: a. 196 b. 216 c. 296 d. 540

Explanation: Juan reads a book with 368 pages and Savannah reads a book with 172 fewer pages than Juan’s which means 368-172= 196 pages are in Savannah’s read.

Question 4. Hailey has bottles that hold 678 pennies each. About how many pennies does she have if she has 6 bottles filled with pennies? Options: a. 3,600 b. 3,900 c. 4,200 d. 6,000

Explanation: Let’s round off 678 to 700 and Hailey has bottles that hold 700 pennies each and if she has 6 bottles filled with pennies which means 700×6= 4200.

Question 5. Terrence plants a garden that has 8 rows of flowers, with 28 flowers in each row. How many flowers did Terrence plant? Options: a. 1,664 b. 224 c. 164 d. 36

Explanation: As the garden has 8 rows of flowers with 28 flowers in each row, So no. of flowers is 28×8= 224.

Question 6. Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin has. How many fish does Jasmine have? Options: a. 15 b. 20 c. 25 d. 30

Explanation: As Kevin has 5 fishes and Jasmine has 4 times as many as Kevin which means 5×4= 20 fishes Jasmine has.

Explanation: 2×36=2×(30+6) =(2×30)+(2×6) =60+12 =72

Question 2. 4 2 × 4 —————- Estimate: _________ Product: _________

Answer: Estimate: 160 Product: 168

Explanation: Round off 42 to 40 and estimated value is 40×4= 160 and 42×4= 168 4 2 × 4 ——- 168

Question 3. 3 2 × 2 —————- Estimate: _________ Product: _________

Answer: Estimate: 60 Product: 64

Explanation: Round off 32 to 30 and the estimated value is 30×2= 60 and 32×2= 64. 3 2 × 2 —— 64

Question 4. 8 1 × 5 —————- Estimate: _________ Product: _________

Answer: Estimate: 400 Product: 405

Explanation: Round off 81 to 80 and the estimated value is 80×5= 400 and 81×5= 405. 81 × 5 —— 405

Question 5. $6 3 × 7 —————- Estimate: $ _________ Product: $ _________

Answer: Estimate: 420 Product: 441

Explanation: Round off 63 to 60 and the estimated value is 60×7= 420 and 63×7= 441. $63 × 7 —— 441

Question 6. 3 3 × 2 —————- Estimate: _________ Product: _________

Answer: Estimate: 60 Product: 66

Explanation: Round off 33 to 30 and the estimated value is 30×2= 60 and 33×2= 66. 3 3 × 2 —— 66

Question 7. $2 5 × 3 —————- Estimate: $ _________ Product: $ _________

Answer: Estimate: 90 Product: 75

Explanation: Round off 25 to 30 and the estimated value is 30×3= 90 and 25×3= 75. $25 × 3 —— 75

Question 8. 3 6 × 8 —————- Estimate: _________ Product: _________

Answer: Estimate: 320 Product: 288

Explanation: Round off 36 to 40 and the estimated value is 40×8= 320 and 36×8= 288. 36 × 8 —— 288

Question 9. $9 4 × 5 —————- Estimate: $ _________ Product: $ _________

Answer: Estimate: 450 Product: 470

Explanation: Round off 94 to 90 and the estimated value is 90×5= 450 and 94×5= 470. $94 × 5 —— 470

Question 10. 3 × 82 Estimate: _________ Product: _________

Answer: Estimate: 240 Product: 246

Explanation: Round off 82 to 80 and the estimated value is 80×3= 240 and 82×3= 246. 3 2 × 2 —— 246

Question 11. 9 × 41 Estimate: _________ Product: _________

Answer: Estimate: 360 Product: 369

Explanation: Round off 41 to 40 and the estimated value is 40×9= 360 and 41×9= 369. 41 ×9 —— 369

Question 12. 7 × $23 Estimate: $ _________ Product: $ _________

Answer: Estimate: 140 Product: 161

Explanation: Round off 23 to 20 and the estimated value is 20×7= 140 and 23×7= 161. 23 × 7 —— 161

Question 13. 8 × $54 Estimate: $ _________ Product: $ _________

Answer: Estimate: 400 Product: 432

Explanation: Round off 54 to 50 and the estimated value is 50×8= 400 and 54×8= 432. 54 ×8 —— 432

Identify Relationships Algebra Write a rule. Find the unknown numbers.

Answer: 36, 60

Explanation: If 1 carton contains 12 eggs then 3 cartons will have 3×12= 36 and 5 cartons contains 5×12= 60.

Answer: 160, 192

Explanation: If 2 rows have 32 seats then 5 rows will have 5×32= 160 and 6 rows will have 6×32= 192 seats

Question 17. It will cost $73 per hour to rent a sailboat and $88 per hour to rent a ski boat. How much more will it cost to rent a ski boat than a sailboat for 4 hours?

Answer: $60.

Explanation: Cost of sailboat to rent per hour is $73 and for 4 hours it costs $73×4= $292. And cost of Ski boat to rent per hour is $88 and for 4 hours it costs $88×4= $352. So $352-$292= $60 much more costs for a ski boat than a sailboat.Problem Solving Multistep Multiplication Problems – Page No. 122

Question 18. At the speeds shown, how much farther could a black-tailed jackrabbit run than a desert cottontail in 7 seconds?

Answer: 203 ft.

Explanation: Black-tailed jackrabbit runs at a speed of 51 ft per sec, So in 7 seconds jackrabbit runs 51×7= 357 ft and Desert cottontail runs at a speed of 22 ft per sec, So in 7 seconds it runs 22×7= 154 ft. So 357-154= 203 ft could a black-tailed jackrabbit run than a desert cottontail in 7 seconds.

Question 19. A black-tailed jackrabbit hops about 7 feet in a single hop. How far can it hop in 5 seconds? about ______ hops

Answer: 35 hops.

Explanation: As black-tailed jackrabbit hops about 7 feet in a single hop, So in 5 seconds it hops 7×5= 35.

Question 20. Mr. Wright bought a 3-pound bag of cat food and a 5-pound bag of dog food. There are 16 ounces in each pound. How many ounces of pet food did Mr. Wright buy?

Answer: 128 ounces.

Explanation: Mr. Wright bought a 3-pound bag of cat food and there are 16 ounces in each pound, So 3×16= 48 ounces and 5pound bag of dog food as 5×16= 80 ounces. So total ounces of pet food are 48+80= 128 ounces.

Question 21. The sum of two numbers is 31. The product of the two numbers is 150. What are the numbers?

Answer: 6 and 25.

Explanation: Let the numbers be X and Y, So the sum of two numbers is 31 which means X+Y=31 and product of two numbers is 150 which means X×Y=150. So X=31-Y then replace X=31-Y, So (31-Y)×Y= 150, then 31Y-Y^ 2 = 150 which is Y^ 2 – 31Y+ 150 = 0. By factorization Y= 25 and X×25= 150 then X= 6. Therefore X= 6 and Y= 25.

Question 22. Use Reasoning 6 × 87 is greater than 5 × 87. How much greater? Explain how you know without multiplying.

Answer: 6×87>5 × 87.

Explanation: As 6 is greater than 5, So 6×87 is greater than 5 × 87

Question 23. Multiply 6 × 73. For 23a–23d, select True or False for each statement. a. A reasonable estimate of the product is $420. i. True ii. False

Answer: False

Explanation: 6×73= 438

Question 23. b. Using partial products, the products are 42 and 180. i. True ii. False

Explanation: The partial products are 420 and 18

Question 23. c. Using regrouping, 18 ones are regrouped as 8 tens and 1 one. i. True ii. False

Answer: False.

Explanation: 8 tens and 1 one means 81.

Question 23. d. The product is 438. i. True ii. False

Answer: True

Question 2. 3 2 × 8 Estimate: ________ Product: ________

Answer: Estimate: 240 Product: 256

Explanation: Round off 32 to 30 and 30×8=240. 3 2 × 8 ———— 256

Question 3. $5 5 × 2 Estimate: $ ________ Product: $ ________

Answer: Estimate: $120 Product: $110

Explanation: Round off 55 to 60 and 60×2= 120. $5 5 × 2 ————- $110

Question 4. 6 1 × 8 Estimate: ________ Product: ________

Answer: Estimate: 480 Product: 488

Explanation: Round off 61 to 60 and 60×8= 480. 6 1 × 8 ———– 488

Question 5. 3 7 × 9 Estimate: ________ Product: ________

Answer: Estimate: 360 Product: 333

Explanation: Round off 37 to 40 and 40×6= 360. 3 7 × 9 ———– 333

Question 6. $1 8 × 7 Estimate: $ ________ Product: $ ________

Answer: Estimate: $140 Product: $126

Explanation: Round off 18 to 20 and 20×7= 140. $1 8 × 7 ———- $126

Question 7. 8 3 × 5 Estimate: ________ Product: ________

Answer: Estimate: 400 Product: 415

Explanation: Round off 83 to 80 and 80×5= 400. 8 3 × 5 ——- 415

Question 8. 9 5 × 8 Estimate: ________ Product: ________

Answer: Estimate: 800 Product: 760

Explanation: Round off 95 to 100 and 100×8= 800. 9 5 × 8 ——– 760

Question 9. 9 4 × 9 Estimate: ________ Product: ________

Answer: Estimate: 810 Product: 846

Explanation: Round off 94 to 90 and 90×9= 810. 9 4 × 9 ——- 846

Question 10. 5 7 × 6 Estimate: ________ Product: ________

Answer: Estimate: 360 Product: 342

Explanation: Round off 57 to 60 and 60×6= 360. 5 7 × 6 —— 342

Question 11. 7 2 × 3 Estimate: ________ Product: ________

Answer: Estimate: 210 Product: 216

Explanation: Round off 72 to 70 and 70×3= 210. 7 2 × 3 ——- 216

Question 12. $7 9 × 8 Estimate: ________ Product: ________

Answer: Estimate: $640 Product: $632

Explanation: Round off 79 to 80 and 80×8= 640. $7 9 × 8 ——- $632

Question 13. Sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is twice as tall as she is. What is the difference, in inches, between the top of the tree and the floor of the treehouse?

Answer: 162 inches.

Explanation: Sharon is 54 inches tall and a tree in her backyard is 5 times as tall as she is which means 54×5= 270. And her treehouse is twice as tall as she is which means 54×2= 108 inches. So the difference between the top of the tree and the floor of the treehouse is 270-108= 162 inches.

Question 14. Mr. Diaz’s class is taking a field trip to the science museum. There are 23 students in the class, and a student admission ticket is $8. How much will the student tickets cost?

Answer: $184.

Explanation: Total no. of students are 23 and tickets cost is $8, So 23×8= $184.

Question 1. A ferryboat makes four trips to an island each day. The ferry can hold 88 people. If the ferry is full on each trip, how many passengers are carried by the ferry each day? Options: a. 176 b. 322 c. 332 d. 352

Explanation: Total trips made by the ferryboat each day are 4 and it can hold 88 people, So 88×4= 352 passengers are carried by ferryboat each day.

Question 2. Julian counted the number of times he drove across the Seven Mile Bridge while vacationing in the Florida Keys. He crossed the bridge 34 times. How many miles in all did Julian drive crossing the bridge? Options: a. 328 miles b. 248 miles c. 238 miles d. 218 miles

Explanation: No. of times Julian drive across the bridge is 7 miles and he crossed the bridge 34 times, So 34×7= 238 miles Julian drive crossing the bridge.

Question 3. Sebastian wrote the population of his city as 300,000 + 40,000 + 60 + 7. Which of the following shows the population of Sebastian’s city written in standard form? Options: a. 346,700 b. 340,670 c. 340,607 d. 340,067

Explanation: 300,000+40,000+60+7= 340,067.

Question 4. A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much farther did the plane that flew to Oakland fly than the plane that flew to Flagstaff? Options: a. 720 kilometers b. 820 kilometers c. 5,000 kilometers d. 5,100 kilometers

Explanation: Plane flew from Chicago to Flagstaff is 2,190 km and another plane flew from Chicago to Oakland is 2,910, So 2910-2190= 720 km.

Question 5. Tori buys 27 packages of miniature racing cars. Each package contains 5 cars. About how many miniature racing cars does Tori buy? Options: a. 15 b. 32 c. 100 d. 150

Explanation: Let’s round off 27 packages to 30 and each package contains 5 cars, which means 30×5=150.

Question 6. Which of the following equations represents the Distributive Property? Options: a. 3 × 4 = 4 × 3 b. 9 × 0 = 0 c. 5 × (3 + 4) = (5 × 3) + (5 × 4) d. 6 × (3 × 2) = (6 × 3) × 2

Answer: Multiplying 4×6

Explanation: In step 1 Multiplying 4×6= 24.

Estimate. Then find the product.

Question 2. 6 0 3 ×   4 ———— 2,400 Estimate: __________ Product: ___________

Answer: Estimate: 2400 Product: 2412

Explanation: Rounding off 603 to 600 then 600×4= 2400. 6 0 3 ×   4 ——– 2412

Question 3. 1,935 ×    7 ———— Estimate: __________ Product: ___________

Answer: Estimate: 14,000. Product: 13,545.

Explanation: Rounding off 1935 to 2000 then 2000×7= 14,000. 1,935 ×    7 ——— 13,545

Question 4. $ 8,326 ×       5 ———— Estimate: $ __________ Product: $ ___________

Answer: Estimate: 40,000 Product: 41,630

Explanation: Rounding off 8326 to 8000 then 8000×5= 40,000. $ 8,326 ×       5 ———- 41,630

Question 5. $ 3,316 ×       8 —————- Estimate: $ __________ Product: $ ___________

Answer: Estimate: 24,000. Product: 26,528.

Explanation: Rounding off 3316 to 3000 then 3000×8= 24,000. $ 3,316 ×       8 ——— 26,528

Question 6. $ 2,900 ×       7 —————– Estimate: $ __________ Product: $ ___________

Answer: Estimate: 21,000. Product: 20,300

Explanation: Rounding off 2900 to 3000 then 3000×7= 21,000. $ 2,900 ×       7 ———- 20,300

Question 7. $ 4,123 ×       6 —————– Estimate: $ __________ Product: $ ___________

Answer: Estimate: 24,000. Product: 24,738

Explanation: Rounding off 4,123 to 4000 then 4000×6= 24,000. $ 4,123 ×       6 ———– 24,738

Question 8. Mr. Jackson has $5,400 to buy supplies for the school computer lab. He buys 8 boxes of printer ink that cost $149 each and 3 printers that cost $1,017 each. How much money will Mr. Jackson have left after he buys the printer ink and printers?

Answer: $1,157

Explanation: As 8 boxes of printer ink cost $149 each which is $149×8=$1,192 and 3 printers costs $1,017 which is $1,017×3=$3,051. So 3051+1192= 4,243 total spent by Mr. Jackson on Printer ink and printers. The money left are $5,400-$4,243= 1,157.

Practice: Copy and Solve Compare. Write <, >, or = .

Question 9. 5 × 352 _____ 4 × 440

Answer: 5 × 352  = 4 × 440

Explanation: As 5 × 352= 1,760 and 4 × 440= 1,760

Question 10. 6 × 8,167 _____ 9,834 × 5

Answer: 6 × 8,167 <  9,834 × 5

Explanation: As 6 × 8,167= 49,002 and 9,834 × 5= 49,170. So 6 × 8,167 <  9,834 × 5

Question 11. 3,956 × 4 _____ 5 × 7,692

Answer: 3,956 × 4 < 5 × 7,692

Explanation: As 3,956 × 4= 15,824 and 5 × 7,692= 38,460. So 3,956 × 4 < 5 × 7,692

Question 12. 740 × 7 _____ 8 × 658

Answer: 740 × 7 < 8 × 658

Explanation:  As 740 × 7 = 5180 and 8 × 658= 5264. So 740 × 7 < 8 × 658

Question 13. 4 × 3,645 _____ 5 × 2,834

Answer: 4 × 3,645 > 5 × 2,834

Explanation: As 4 × 3,645= 14580 and 5 × 2,834= 14,170. So 4 × 3,645 > 5 × 2,834.

Question 14. 6,573 × 2 _____ 4,365 × 3

Answer: 6,573 × 2 > 4,365 × 3

Explanation: As 6,573 ×2= 13,146 and 4,365 × 3= 13,095. So 6,573 × 2 > 4,365 × 3.

Question 15. Airplane tickets to Fairbanks, Alaska, will cost $958 each. Airplane tickets to Vancouver, Canada, will cost $734. How much can the four members of the Harrison family save on airfare by vacationing in Vancouver?

Answer: $896.

Explanation: Airplane tickets cost for Alaska is $958 each. As Harrison family are 4 members so it will cost $958×4= $3,832 And for Vancouver it costs $734 each. So $734×4= $2,936 and Harrison family save $3832-$2936= $896.

Question 16. Philadelphia, Pennsylvania, is 2,147 miles from Salt Lake City, Utah, and 2,868 miles from Portland, Oregon. What is the difference in the round-trip distances between Philadelphia and each of the other two cities? Explain whether you need an estimate or an exact answer.

Answer: 1,442 mi.

Explanation: The distance between Philadelphia and Salt Lake is 2,147 miles and round-trip distance is 2×2,147= 4,294 miles. And the distance between Philadelphia and Portland is 2,868 miles and the round-trip distance is 2×2868= 5736 miles. So the difference is 5,736-4,294= 1442 miles.

Question 17. Verify the Reasoning of Others Joe says that the product of a 4-digit number and a 1-digit number is always a 4-digit number. Does Joe’s statement make sense? Explain.

Answer: No, Joe’s statement is incorrect.

Explanation: As there are regrouped thousands, the product of a 4-digit number and a 1-digit number can have 5 digits.

Question 18. What number is 150 more than the product of 5 and 4,892? Explain how you found the answer.

Answer: 24,610.

Explanation: Let’s find the product of 5×4,892= 54,460 and then add 150 to the product, So 24,460+150= 24,610.

Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 129

Question 2. 5,339 ×    6 ————- Estimate: ________ Product: ________

Answer: Estimate: 30,000 Product: 32,034

Explanation: Round off 5,339 to 5000 then 5000×6= 30,000. 5,339 ×    6 ———- 32,034

Question 3. $879 ×   8 ————- Estimate: $ ________ Product: $ ________

Answer: Estimate: $7,200. Product: $7,032.

Explanation: Round off 879 to 900 then 900×8= 7,200. $879 ×   8 ——– 7,032

Go Math Lesson 2.11 4th Grade Question 4. 3,182 ×    5 ————- Estimate: ________ Product: ________

Answer: Estimate: 15,000 Product: 15,910

Explanation: Round off 3,182 to 3000 then 3000×5= 15,000. 3,182 ×    5 ———- 15,910

Question 5. 4,616 ×    3 ————- Estimate: ________ Product: ________

Answer: Estimate: 15,000 Product: 13,848

Explanation: Round off 4,616 to 5,000 then 5000×3= 15,000. 4,616 ×    3 ——— 13,848

Question 6. 2,854 ×    9 ————- Estimate: ________ Product: ________

Answer: Estimate: 27,000 Product: 25,686

Explanation: Round off 2,854 to 3000 then 3000×9= 27,000. 2,854 ×    9 ——— 25,686

Question 7. 7,500 ×    2 ————- Estimate: ________ Product: ________

Answer: Estimate: 16,000 Product: 15,000

Explanation: Round off 7,500 to 8000 then 8000×2= 16,000. 7,500 ×    2 ——— 15,000

Question 8. 9 4 8 ×   7 ————- Estimate: ________ Product: ________

Answer: Estimate: 6,300 Product: 6,636

Explanation: Explanation: Round off 948 to 900 then 900×7= 6,300. 9 4 8 ×   7 ——- 6,636

Question 9. 1,752 ×    6 ————- Estimate: ________ Product: ________

Answer: Estimate: 12,000. Product: 10,512.

Explanation: Explanation: Round off 1,752 to 2000 then 2000×6= 12,000. 1,752 ×    6 ———– 10,512

Question 10. 5 5 0 ×   9 ————- Estimate: ________ Product: ________

Answer: Estimate: 5,400 Product: 4,950

Explanation: Round off 550 to 600 then 600×9= 5,400. 5 5 0 ×   9 ——– 4,950

Question 11. 6,839 ×    4 ————- Estimate: ________ Product: ________

Answer: Estimate: 28,000 Product: 27,356

Explanation: Round off 6,839 to 7000 then 7000×4= 28,000. 6,839 ×    4 ———- 27,356

Question 12. $9,614 ×      6 ————- Estimate: $ ________ Product: $ ________

Answer: Estimate: 60,000. Product: 57,684.

Explanation: Round off 9,614 to 10,000 then 10,000×6= 60,000. $9,614 ×      6 ———- 57,684

Question 13. Lafayette County has a population of 7,022 people. Columbia County’s population is 8 times as great as Lafayette County’s population. What is the population of Columbia County?

Answer: 56,176 people

Explanation: Lafayette County has a population of 7,022 people and Columbia County’s population is 8 times Lafayette County which means 7,022×8= 56,176.

Question 14. A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all?

Answer: 54,750 pounds.

Explanation: As the seafood company sold 9,125 pounds of fishes last month and 6 seafood companies also sold the same amount which means 9,125×6= 54,750 pounds.

Question 1. By recycling 1 ton of paper, 6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper? Options: a. 24,602 gallons b. 27,612 gallons c. 27,812 gallons d. 28,000 gallons

Explanation: As 1 ton of paper saves 6,953 gallons of water, So 4 tons of paper can save 6,953×4= 27,812.

Question 2. Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps. How many steps does he take walking to and from school each day? Options: a. 2,000 b. 2,266 c. 2,276 d. 22,616

Explanation: As Esteban counted 1,138 steps to school and from school, it will be 1,138+1,138=2,276 steps

Question 3. A website has 13,406 people registered. What is the word form of this number? Options: a. thirty thousand, four hundred six b. thirteen thousand, four hundred sixty c. thirteen thousand, four hundred six d. thirteen thousand, six hundred six

Explanation: 13,406 in words are thirteen thousand four hundred six.

Question 4. In one year, the McAlister family drove their car 15,680 miles. To the nearest thousand, how many miles did they drive their car that year? Options: a. 15,000 miles b. 15,700 miles c. 16,000 miles d. 20,000 miles

Explanation: 15,680 nearest thousand is 16,000

Question 5. Connor scored 14,370 points in a game. Amy scored 1,089 fewer points than Connor. How many points did Amy score? Options: a. 12,281 b. 13,281 c. 15,359 d. 15,459

Explanation: Connor scored 14,370 points and Amy scored 1,089 fewer points, So Amy score is 14,370-1089= 13,281.

Question 6. Lea buys 6 model cars that each cost $15. She also buys 4 bottles of paint that each cost $11. How much does Lea spend in all on model cars and paint? Options: a. $134 b. $90 c. $44 d. $36

Explanation: Lea buys 6 model cars that each cost $15, So the total cost for cars is $15×6= $90. And 4 bottles of paint that each cost $11, So the total cost of paints is $11×4= $44. Then $90+$44= $134.

Question 1. Use the order of operations to find the value of n. 5 × 17 + 5 × 20 – 32 = n n = ______

Answer: 153

Explanation: (5×17)+5×20 –32= = 85+100-32 =185-32 =153

Find the value of n.

Question 2. 3 × 22 + 7 × 41 – 24 = n n = ______

Answer: 329.

Explanation: 3×22+7×41–24 =66+287-24 =329.

Question 3. 4 × 34 + 6 × 40 – 66 = n n = ______

Answer: 310.

Explanation: 4×34+6×40–66= =136+240-66 =310.

Question 4. 2 × 62 + 8 × 22 – 53 = n n = ______

Answer: 247

Explanation: 2×62+8×22–53= = 124+176-53 =300-53 =247.

Question 5. 6 × 13 + 9 × 34 – 22 = n n = ______

Answer: 362.

Explanation: 6×13+9×34–22= =78+306-22 =384-22 =362.

Question 6. 8 × 42 + 3 × 59 – 62 = n n = ______

Answer: 451.

Explanation: 8×42+3×59–62= =336+177-62 =513-62 =451.

Question 7. 6 × 27 + 2 × 47 – 83 = n n = ______

Answer: 173

Explanation: 6×27+2×47–83= =162+94-83 =256-83 =173

Question 8. Maggie has 3 binders with 25 stamps in each binder. She has 5 binders with 24 baseball cards in each binder. If she gives 35 stamps to a friend, how many stamps and cards does she have left?

Answer: 160

Explanation: Maggie has 3 binders with 25 stamps each binder, so total stamps are 3×25= 75. And 5 binders with 24 baseball cards in each binder. So total baseball cards are 24×5=120. As she gave 35 stamps to a friend, so 75-35= 40. Total stamps and cards she has 120+40= 160

Question 9. Evaluate Maddox has 4 boxes with 32 marbles in each box. He has 7 boxes with 18 shells in each box. If he gets 20 marbles from a friend, how many marbles and shells does he have?

Explanation: Maddox has 4 boxes and 32 marbles in each box, so 4×32= 128. And 7 boxes with 18 shells in each box which means 7×18= 126. And he got 20 marbles from a friend, so 128+20= 148 marbles. So total marbles and shells he has 148+126= 274.

Question 10. The soccer team sells 54 bagels with cream cheese for $2 each and 36 muffins for $1 each during a bake sale. The coach uses the money to buy socks for the 14 players. The socks cost $6 per pair. How much money does the coach have left? Explain how you found your answer.

Explanation: Soccer team sells 54 bagels with cream cheese for $2 each, so 54×2= $108 total amount raised by selling bagels with cream cheese. And 36 muffins for $1 each which means 36×$1= $36 raised by selling muffins. So the total amount raised is $108+$36= $144. And he uses the money to buy socks for 14 players and each pair is $6, So 14×$6= $84 needed to buy socks for the players. So $144-$84= $60 left with the coach after buying socks for the players.

Answer: Dominic didn’t follow the order of operations

Question 11. Use the correct steps to solve the problem.

Answer: 5 × 12 + 4 × 20 – 15 = n 60+4×20-15=n 60+80-15=n 140-15=n 125=n

Common Core – Solve Multistep Problems Using Equations – Page No. 135

Question 1. 4 × 27 + 5 × 34 – 94 = n 108 + 5 × 34 – 94 = n 108 + 170 – 94 = n 278 – 94 = n 184 = n

Question 2. 7 × 38 + 3 × 45 – 56 = n _____ = n

Answer: 345.

Explanation: 7×38+3×45-56= =266+135-56 =401-56 =345

Question 3. 6 × 21 + 7 × 29 – 83 = n _____ = n

Answer: 246

Explanation: 6×21+7×29-83= =126+203-83 =329-83 =246

Question 4. 9 × 19 + 2 × 57 – 75 = n _____ = n

Answer: 210.

Explanation: 9×19+2×57-75= =171+114-75 =285-75 =210.

Question 5. 5 × 62 + 6 × 33 – 68 = n _____ = n

Answer: 440.

Explanation: 5 × 62 + 6 × 33 – 68= =310+198-68 =508-68 =440

Question 6. 8 × 19 + 4 × 49 – 39 = n _____ = n

Answer: 309

Explanation: 8×19+4×49-39= =152+196-39 =348-39 =309

Question 7. A bakery has 4 trays with 16 muffins on each tray. The bakery has 3 trays of cupcakes with 24 cupcakes on each tray. If 15 cupcakes are sold, how many muffins and cupcakes are left?

Answer: 121 muffins and cupcakes.

Explanation: 4×16+3×24-15=n 64+3×24-15=n 64+72-15=n 136-15=n 121=n

Question 8. Katy bought 5 packages of stickers with 25 stickers in each package. She also bought 3 boxes of markers with 12 markers in each box. If she receives 8 stickers from a friend, how many stickers and markers does Katy have now?

Answer: 169 stickers and markers.

Explanation: 5×25+3×12+8=n 125+3×12+8=n 125+36+8=n 169=n

Question 1. What is the value of n? 9 × 23 + 3 × 39 – 28 = n Options: a. 240 b. 296 c. 2,310 d. 8,162

Answer: 296

Explanation: 9×23+3×39–28= =207+117-28 =324-28 =296

Question 2. Which expression has a value of 199? Options: a. 4 × 28 + 6 × 17 – 15 b. 4 × 17 + 6 × 28 – 38 c. 4 × 38 + 6 × 15 – 28 d. 4 × 15 + 6 × 38 – 88

Explanation: 4×28+6×17-15= =112+102-15 =214-15 =199.

Question 3. Which expression shows how you can multiply 9 × 475 using expanded form and the Distributive Property? Options: a. (9 × 4) + (9 × 7) + (9 × 5) b. (9 × 4) + (9 × 70) + (9 × 700) c. (9 × 400) + (9 × 70) + (9 × 5) d. (9 × 400) + (9 × 700) + (9 × 500)

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. 9 × 475= (9×400)+(9×70)+(9×5)

Question 4. Which equation best represents the comparison sentence? 32 is 8 times as many as 4 Options: a. 32 = 8 × 4 b. 32 × 8 = 4 c. 32 = 8 + 4 d. 8 + 4 = 32

Explanation: 32=8×4

Question 5. Between which pair of numbers is the exact product of 379 and 8? Options: a. between 2,400 and 2,500 b. between 2,400 and 2,800 c. between 2,400 and 3,000 d. between 2,400 and 3,200

Explanation: 379×8= 3,032

Question 6. Which of the following statements shows the halving and doubling strategy to find 28 × 50? Options: a. 28 × 50 = 14 × 100 b. 28 × 50 = (14 × 25) × (14 × 25) c. 28 × 50 = (20 × 50) × (8 × 50) d. 28 × 50 = 2 × (14 × 25)

Explanation: 28×50 = 14×100

Question 1. What is the cost of 3 Bur Oak trees? Show your work.

Answer: $96.

Explanation: Each Bur oak tree costs $32 for 3 and above, so $32×3=$96.

Question 2. Mr. Tan buys 4 White Pine trees and 5 Birch trees. What is the cost of the trees? Show your work and explain how you found the answer.

Answer: $188.

Explanation: As 4 white pine trees cost is $37 each, so $37×4= $148 and 5 birch trees cost $8 each, so 5×$8= $40. Total cost of trees are $148+$40= $188.

Question 3. Rudy will buy 3 Ivory Silk Lilac trees or 2 Bur Oak trees. He wants to buy the trees that cost less. What trees will he buy? How much will he save? Show your work.

Answer: Rudy will take 3 Ivory Silk Lilac trees which costs $66.

Explanation: If Rudy buys 3 Ivory Silk Lilac trees which costs $22 each, so $22×3=$66. And if 2 Bur Oak trees price is $35 each which means $35×2= $70. As Rudy wants to buy the trees that cost less, so he will take 3 Ivory Silk Lilac trees which cost $66.

Question 4. For numbers 4a–4d, select True or False for each equation. a. 7 × 194 = 1,338 i. True ii. False

Explanation: 7×194= 1,338.

Question 4. b. 5 × 5,126 = 25,630 i. True ii. False

Explanation: 5×5,126= 25,630.

Question 4. c. 8 × 367 = 2,926 i. True ii. False

Explanation: 8×367= 2,936

Question 4. d. 4 × 3,952 = 15,808 i. True ii. False

Explanation: 4×3952= 15,808

Question 5. Part B Then find 3 × 146. Show your work and explain.

Answer: 438.

Explanation: By distributive property 3×146= 3×(100+40+6) =(3×100)+(3×40)+( 3×6) =300+120+18 =438.

Answer: 8 times as many as 4 is 32.

Answer: 6 times as many as 8 is 48.

Explanation: 6×8= 48.

Question 6. c. 9 × 3 = 27 ______ times as many as ______ is ______ .

Answer: 9 times as many as 3 is 27

Question 7. Multiply 7 × 43. For 7a–7d, select True or False for each statement. a. A reasonable estimate of the product is 280. i. True ii. False

Explanation: 7×43= 301. Take 43 and round off to 40 then 40×7= 280.

Question 7. b. Using partial products, the products are 21 and 28. i. True ii. False

Explanation: 7×43= 7×(40+3) =(7×40)+(7×3) =280+21. So partial products are 280 and 21.

Question 7. c. Using regrouping, 21 ones are regrouped as 1 ten and 2 ones. i. True ii. False

Explanation: 1 ten and 2 ones is 12

Question 7. d. The product is 301. i. True ii. False

Answer: True.

Explanation: 7×43= 7×(40+3) =(7×40)+(7×3) =280+21 =301.

Question 8. It costs 9,328 points to build each apartment building in the computer game Big City Building. What is the cost to build 5 apartment buildings? Show your work.

Answer: 46,640 points.

Explanation: The cost of each building apartment is 9,328 points. To build 5 apartments its costs 9,3287×5= 46,640 points.

Answer: 400, 60, 2

Explanation: 7×462= 7×(400+60+2).

Question 10. For numbers 10a–10b, use place value to find the product. a. 3 × 600 = 3 × ______ hundreds = ______ hundreds ______

Answer: 6 hundreds, 18 hundreds , 1800

Explanation: 3 × 600 = 3 × 6 hundreds = 18 hundreds = 1800.

Question 10. b. 5 × 400 = 5 × ______ hundreds ______ hundreds ______

Answer: 4hundreds, 20hundreds, 2,000.

Explanation: 5 × 400 = 5 × 4hundreds = 20 hundreds = 2,000.

Question 11. Liam has 3 boxes of baseball cards with 50 cards in each box. He also has 5 boxes with 40 basketball cards in each box. If Liam goes to the store and buys 50 more baseball cards, how many baseball and basketball cards does Liam have? Show your work.

Answer: Liam has 400 baseball and baseball cards.

Explanation: Liam has 3 boxes of baseball cards and there are 50 cards in each box, so total cards are 50×3= 150 baseball cards. And he has 5 boxes with 40 baseball cards in each box which means 5×40= 200. So total baseball cards are 150+200= 350. And he went to the store to buy 50 more baseball cards, so total baseball cards are 350+50= 400.

Answer: 200, 80, 9.

Explanation: As the price of each book is $4, so for 289 books it will be 4×289 = 4×(200+80+9) =(4×200)+(4×80)+(4×9) =800+320+36 =1,156.

Question 13. Find 8 × 397. Show your work and explain why the strategy you chose works best with the factors.

Answer: 3,176.

Explanation: 8×397= 8×(300+90+7) =(8×300)+(8×90)+(8×7) =2400+720+56 =3,176.

Question 14. A clown bought 6 bags of round balloons with 24 balloons in each bag. The clown also bought 3 bags of long balloons with 36 balloons in each bag. Part A How many more long balloons than round balloons did the clown buy? Show your work. ______ balloons

Answer: 36.

Explanation: As clown bought 6 bags of round balloons with 24 balloons in each bag, so 6×24= 144 and 3 bags of long balloons with 36 balloons in each bag, so 3×36= 108, So 144-108= 36.

Question 14. Part B The clown also bought 5 bags of heart-shaped balloons with 14 balloons in each bag. When the clown blew up all of the round, long, and heart-shaped balloons, 23 balloons burst. How many blown-up balloons were left? Explain your answer. ______ blown-up balloons

Answer: 299.

Explanation: The no. of heart-shaped balloons 5×14= 70. Then add that number to the number of round balloons and long balloons 70+144+108= 322 balloons in all. Then subtract the number of burst balloons, so 322-23= 299 balloons left.

Answer: 1000.

Explanation: Hector planted 185 flowers in 2 days, so 5 volunteers can plant 185×5= 925.

Question 16. Jay and Blair went fishing. Together, they caught 27 fish. Jay caught 2 times as many fish as Blair. How many fish did Jay and Blair each catch? Write an equation and solve. Explain your work. Jay: ______ fish;         Blair: ______ fish

Answer: Blair caught 9 fishes and Jay caught 18 fishes.

Explanation: Blair caught n fish and Jay caught 2×n fish. Together they caught 3×n fish, so 3×n= 27 and n= 9 fishes, and 2×n= 18 fishes. Blair caught 9 fishes and Jay caught 18 fishes

Answer: Leah’s dog is 14 pound and Darlene’s dog weight is 70 pounds.

Answer: 4×12= 48.

Explanation: 4×12=4×(10+2) =(4×10)+(4×2) =40+8 =48

Question 1. Find 20 × 27. Tell which method you chose. Explain what happens in each step.

Explanation: It is mental maths. Because 2×27= 54 and 20×27= 540.

Choose a method. Then find the product.

Question 2. 10 × 12 = ______

Answer: 120

Explanation: Mental math, as 1×12=12 and 10×12= 120

Question 3. 20 × 20 = ______

Answer: 400

Explanation: Mental math, as 2×2=4 and 20×20= 400

Question 4. 40 × 24 = ______

Answer: 960

Explanation: Mental math, as 4×24=96 and 40×24= 960

Question 5. 11 × 60 = ______

Answer: 660

Explanation: Mental math, as 11×6=66 and 11×60= 660

Question 6. 70 × 55 = ______

Answer: 3850

Explanation: Mental math, as 7×55=385 and 70×55= 3850

Question 7. 17 × 30 = ______

Answer: 510

Explanation: Mental math, as 17×3=51 and 17×30= 510

Question 8. 30 × 60 = ______

Answer: 1800

Explanation: Mental math, as 30×60=1800 and 30×60= 1800

Question 9. 12 × 90 = ______

Answer: 1080

Explanation: Mental math, as 12×9=108 and 12×90= 1080.

Reason Quantitatively Algebra Find the unknown digit in the number.

Question 10. 64 × 40 = 2,56■ ■ = ______

Answer: 2,560

Explanation: Mental math, as 64×4=256 and 64×40= 510

Question 11. 29× 50 = 1,★50 ★ = ______

Explanation: Mental math, as 29×5=145 and 29×50= 1450

Question 12. 3⧫× 47 = 1,410 ⧫ = ______

Explanation: Mental math, as 3×47=1410 and 30×47= 1410

Question 13. Caroline packs 12 jars of jam in a box. She has 40 boxes. She has 542 jars of jam. How many jars of jam will she have left when all the boxes are full?

Answer: 62 jars.

Explanation: Caroline packs 12 jars in a box and she has 40 boxes, so total boxes are 12×40= 480 boxes. As she has 542 jars of jam, so total jars left are 542-480= 62 jars.

Question 14. Alison is preparing for a math contest. Each day, she works on multiplication problems for 20 minutes and division problems for 10 minutes. How many minutes does Alison practice multiplication and division problems in 15 days?

Answer: 450 mins.

Explanation: As Alison works on multiplication problems for 20 mins and 10 mins on division problems, So total time taken by Alison is 20+10=30 mins. So for 15 days Alison takes 15×30= 450 mins.

Question 15. Use Graphs How many frames did it take to produce 50 seconds of Pinocchio?

Answer: 950 Frames.

Explanation: Total frames are 50×19= 950 frames.

Question 16. Are there fewer frames in 10 seconds of The Flintstones or in 14 seconds of The Enchanted Drawing? What is the difference in the number of frames?

Explanation: The Flintstone frames in 10 seconds are 10×24= 240 and The Enchanted Drawing frames are 14×20= 280. So the difference between them is 280-240= 40.

Question 17. The product of my number and twice my number is 128. What is half my number? Explain how you solved the problem.

Explanation: First make a table to test numbers less than 10 since 10×20= 200, and 2×8= 16 then 8×16= 128 and 8÷2= 4.

Question 18. Tanya says that the product of a multiple of ten and a multiple of ten will always have only one zero. Is she correct? Explain.

Explanation: The product of two multiples of ten will always have at least 2 zeros.

Question 19. For numbers 19a–19e, select Yes or No to tell whether the answer is correct. a. 28 × 10 = 280 i. yes ii. no

Answer: Yes

Question 19. b. 15 × 20 = 300 i. yes ii. no

Question 19. c. 17 × 10 = 17 i. yes ii. no

Question 19. d. 80 × 10 = 800 i. yes ii. no

Question 19. e. 16 × 30 = 1,800 i. yes ii. no

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