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Fraction Worksheets

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

• Download the set

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

Related Worksheets

» Decimal Word Problems

» Ratio Word Problems

» Division Word Problems

» Math Word Problems

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Word Problems on Fraction

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

I. Word Problems on Addition of Fractions:

1. Nairitee took \(\frac{7}{8}\) hour to paint a table and \(\frac{2}{3}\) hour to paint a chair. How much time did he take in painting both items?

Total time taken in painting both items = \(\frac{7}{8}\) h + \(\frac{2}{3}\) h                                                          = (\(\frac{7}{8}\) + \(\frac{2}{3}\)) h

                                                         = (\(\frac{21 + 16}{24}\)) h

                                                         = \(\frac{37}{24}\) h

                                                         = 1\(\frac{13}{24}\) h

Therefore, Nairitee took 1\(\frac{13}{24}\) hours in painting both items.

2. Nitheeya and Nairitee \(\frac{3}{10}\) and \(\frac{1}{6}\) of a cake respectively. What portion of the cake did they eat together? 

The portion of cake ate by Nitheeya = \(\frac{3}{10}\)

The portion of cake ate by Nitheeya = \(\frac{1}{6}\)  The portion they ate together = \(\frac{3}{10}\) + \(\frac{1}{6}\) 

                                           = \(\frac{9}{30}\) + \(\frac{5}{30}\); [Since, LCM of 10 and 6 = 30]

                                           = \(\frac{9 + 5}{30}\)

                                           = \(\frac{14}{30}\)

                                           = \(\frac{7}{15}\)

Therefore, together Nitheeya and Nairitee ate \(\frac{7}{15}\) of the cake.

3.  Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?

II. Word Problems on Subtraction of Fractions:

1.  Out of \(\frac{12}{17}\)  m  of cloth given to a tailor, \(\frac{1}{5}\)  m  were used. Find the length of cloth unused. 

Length of the cloth given to the tailors = \(\frac{12}{17}\)  m

Length of cloth used = \(\frac{1}{5}\)  m

Length of the unused cloth = \(\frac{12}{17}\)  m -  \(\frac{1}{5}\)  m

                                        = (\(\frac{12}{17}\)  -  \(\frac{1}{5}\))  m

                                        = (\(\frac{12 × 5}{17 × 5}\)  -  \(\frac{1 × 17}{5 × 17}\))  m;  [Since, LCM of 17 and 5 = 85]

                                        = (\(\frac{60}{85}\)  -  \(\frac{17}{85}\))  m

                                        = (\(\frac{60 - 17}{85}\)  m

                                        = (\(\frac{43}{85}\)  m

2.  Nairitee has $6\(\frac{4}{7}\). She gives $4\(\frac{2}{3}\) to her mother. How much money does she have now?

Money with Nairitee = $6\(\frac{4}{7}\)

Money given to her mother = $4\(\frac{2}{3}\)

Money left with Nairitee = $6\(\frac{4}{7}\) - $4\(\frac{2}{3}\)

                                   = $(6\(\frac{4}{7}\) - 4\(\frac{2}{3}\))

                                   = $(\(\frac{46}{7}\) - \(\frac{14}{3}\))

                                   = $(\(\frac{46 × 3}{7 × 3}\) - \(\frac{14 × 7}{3 × 7}\)) ;  [Since, LCM of 7 and 3 = 21]

                                   = $(\(\frac{138}{21}\) - \(\frac{98}{21}\))

                                   = $\(\frac{40}{21}\)

                                   = $1\(\frac{19}{21}\)

Therefore, Nairitee has $1\(\frac{19}{21}\).

3.  If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m

Length of the wire left = 10 m – 3\(\frac{1}{2}\) m

            = [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m,    [L.C.M. of 1, 2 is 2]

            = [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m,    [\(\frac{10}{1}\) × \(\frac{2}{2}\)]

            = [\(\frac{20 - 7}{2}\)] m

            = \(\frac{13}{2}\) m

            = 6\(\frac{1}{2}\) m

III. Word Problems on Multiplication of Fractions:

1.  \(\frac{4}{7}\) of a number is 84. Find the number. Solution: According to the problem, \(\frac{4}{7}\) of a number = 84 Number = 84 × \(\frac{7}{4}\) [Here we need to multiply 84 by the reciprocal of \(\frac{4}{7}\)]

= 21 × 7 = 147 Therefore, the number is 147.

2.  One half of the students in a school are girls, \(\frac{3}{5}\) of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Fraction of girls studying in school = \(\frac{1}{2}\)

Fraction of girls studying in lower classes = \(\frac{3}{5}\) of \(\frac{1}{2}\)

                                                            = \(\frac{3}{5}\) × \(\frac{1}{2}\)

                                                            = \(\frac{3 × 1}{5 × 2}\)

                                                            = \(\frac{3}{10}\)

Therefore, \(\frac{3}{10}\) of girls studying in lower classes.

3.  Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = \(\frac{3}{5}\) of 75 = \(\frac{3}{5}\) × 75

= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages.

IV. Word Problems on Division of Fractions:

1.  A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?

Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = \(\frac{1}{3}\) of 4 Therefore, each cow gives \(\frac{4}{3}\) of milk each day. Total no. of cows = 4 ÷ \(\frac{4}{3}\)                          = 4 × \(\frac{3}{4}\)                          = 3 Therefore there are 3 cows in the herd.

Worksheet on Word problems on Fractions:

1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?

3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?

4. Between 4\(\frac{2}{3}\)and 3\(\frac{2}{3}\) which is greater and by how much?

5. What must be subtracted from 5\(\frac{1}{6}\) to get 2\(\frac{1}{8}\)?

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●   Multiplication is Repeated Addition.

●  Multiplication of Fractional Number by a Whole Number.

●  Multiplication of a Fraction by Fraction.

●  Properties of Multiplication of Fractional Numbers.

●  Multiplicative Inverse.

●  Worksheet on Multiplication on Fraction.

●  Division of a Fraction by a Whole Number.

●  Division of a Fractional Number.

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●  Properties of Fractional Division.

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Word Problems with Fractions

Today we are going to look at some examples of word problems with fractions.

Although they may seem more difficult, in reality, word problems involving fractions are just as easy as those involving whole numbers. The only thing we have to do is:

• Read the problem carefully.
• Think about what it is asking us to do.
• Think about the information we need.
• Simplify, if necessary.
• Think about whether our solution makes sense (in order to check it).

As you can see, the only difference in fraction word problems is step 5 (simplify) .

There are some word problems which, depending on the information provided, we should express as a fraction.  For example:

In my fruit basket, there are 13 pieces of fruit, 5 of which are apples. 

How can we express the number of apples as a fraction?

5 – The number of apples (5) corresponds to the numerator (the number which expresses the number of parts that we wish to represent).

13 – The total number of fruits (13) corresponds to the denominator (the number which expresses the number of total possible parts).

The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do.

Word problems with fractions: involving two fractions

In these problems, we should remember how to carry out operations with fractions.

Carefully read the following problem and the steps we have taken to solve it:

What fraction of the payment has Maria spent?

We find the common denominator:

We calculate:

Word problems with fractions: involving a fraction and a whole number

Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate

  We convert 1 into a fraction with the same denominator:

What do you think of this post? Do you see how easy it is to solve word problems with fractions?

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Learn More:

• Understand What a Fraction Is and When It Is Used
• Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
• Learn and Practice How to Subtract or Add Fractions
• Learn How to Subtract Fractions
• Review and Practice the Two Methods of Dividing Fractions
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39 Comments

I loved the word problem

Thanks for your help

it simplifies the teaching and learning process

Thanks for the explanation… really grateful 🙏

Thank you for such good explanations, it helped me a lot

It is really good it helped me improve my math a lot.

same it helps me in my math too

Wow, it really helps a lot

Good exercises

Interesting

wow it worked

Hi can you not show the answer till the bottom of the page or your giving away the answer so if you solved number one problem the number one aware to the question will be there at the bottom of the page because it is way to easy if it is right there

I like that you are doing for as Thank you

I really want to be part of this

wow, this help me a lot

A big help for my kids lesson

Thank for helping me

Thank you for all the homework you have given us. God bless you

Thank you for this problems that involved fractions

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Please help me with my math homework

Hi Letlhogonolo,

Thank you very much for your comment. If you want to learn more content like this and practice elementary school math, just sign up at Smartick . You have a free trial period with no strings attached. If you have any additional questions or doubts you can write to my colleagues of the pedagogical team at [email protected] .

Best regards!

I like it… but you can level up please 🙄

Roll two dices, the first dice is the numerator, the second is the denominator, this is the first fraction. Roll both dices again and repeat the process to generate the second fraction. Write a division story problem that incorporates these two fractions.

Seems easy of the examples but when I have fraction word promblems in front of me then its still hard for me to figure it out.The examples on this site still is helpful.I will use the site that you give on here to get further practice.Thank you for the examples on here

Interesting and very helpful. I’m going to continue using this site and tell others about it too.

I really like it

Hey I am in grade five and it is super helpful for my exams thanks and maybe if you could make more it would be appriciated thx 🙂

Good efforts

i kinda like it pls write some more problems

I think it was really good how you are helping fellow students! But I think you can improve if there were more problems for solving! Thanks

Cool, it helps a lot.

it is helpfull

Fractions Questions

Fractions questions are given here will help the students to understand how to perform arithmetic operations on fractions. We know that fractions is one of the most important concepts of Class 7 Maths. In this article, you will get the questions on fractions, along with their solutions, based on the latest NCERT curriculum.

What are Fractions?

In maths, a fraction is defined as a part of the whole thing, and it can be written in the form a/b, where a and b are whole numbers, also, b ≠ 0. Based on the numerical values of numerator and denominator, we can define different types of fractions .

Proper fraction: A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.

Improper fraction: An improper fraction is a number in which the numerator is greater than the denominator.

Mixed fraction: A mixed fraction is a combination of a whole number and a proper fraction.

Learn more about fractions here.

Fractions Questions and Answers

1. How many 2/3 kg pieces can be cut from a cake of weight 4 kg?

Let p be the number 2/3 kg pieces that are cut from a 4 kg cake.

So, p × (2/3) = 4

p = 4 × (3/2)

Therefore, six 2/3 kg pieces can be cut from a cake of weight 4 kg.

2. What is the product of 5/129 and its reciprocal?

Given fraction: 5/129

Here, numerator = 5

Denominator = 129

Reciprocal of 5/129 = 129/5

The product of 5/129 and its reciprocal = (5/129) × (129/5) = 1.

3. Sunita and Rehana want to make dresses for their dolls. Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana. How much did Rehana have?

Length of cloth Sunita has = 3/4 m

According to the given,

Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana.

Therefore, the length of cloth Rehana has

= 1/3 of 3/4 m

= (1/3) x (3/4) m

4. Anuradha can do a piece of work in 6 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours?

Let m be the whole work to be done.

The part of work done by Anuradha in 6 hours = m

Thus, the part of work done by her in 1 hour = m/6

The part of work done by her in 5 hours = (m/6) x 5 = 5m/6

The part of work done by her in 6 hours = (m/6) x 6 = m

Therefore, Anuradha can do 1/6 part of work in 1 hour, 5/6 part of work in 5 hours and the complete work in 6 hours.

5. Multiply the following fractions.

(i) (⅖) × 5 ¼

(ii) 2 ⅗ × 3

Here, 5 ¼ is a mixed fraction.

Let us convert this mixed fraction into an improper fraction.

5 ¼ = [(5 × 4) + 1]/4 = 21/4

Thus, (⅖) × 5 ¼ = (⅖) × (21/4) = 21/10

Here, 2 ⅗ is a mixed fraction.

2 ⅗ = [(2 × 5) + 3]/5 = 13/5

Therefore, 2 ⅗ × 3 = (13/5) × 3 = 39/5

6. Divide 3/10 by (1/4 of 3/5).

1/4 od 3/5 = (1/4) × (3/5) = 3/(4 × 5) = 3/20

3/10 ÷ (1/4 of 3/5)

= 3/10 ÷ 3/20

= (3/10) × (20/3)

\(\begin{array}{l}\text{7. Find the value of }\frac{1}{4\frac{2}{7}}+\frac{1}{3\frac{11}{13}}\frac{1}{\frac{5}{9}}.\end{array} \)

First, simplify the denominators.

= (7/30) + (13/50) + (9/5)

= (35 + 39 + 270)/150 {since the LCM of 30, 50 and 5 is 150}

8. Evaluate the following:

(i) 3 ½ ÷ 4

(ii) 4 ⅓ ÷ 3

Here, 3 ½ is a mixed fraction.

3 ½ = (3 × 2 + 1)/2 = 7/2

3 ½ ÷ 4 = 7/2 ÷ 4 = (7/2) × (¼) = 7/8

Here, 4 ⅓ is a mixed fraction.

4 ⅓ = (4 × 3 + 1)/3 = 13/3

4 ⅓ ÷ 3 = 13/3 ÷ 3 = (13/3) × (⅓) = 13/9

9. 1/8 of a number equals 2/5 ÷ 1/20. What is the number?

Let p be the number.

(1/8) × p = 2/5 ÷ 1/20

p/8 = (2/5) × (20/1)

p/8 = 2 × 4

Hence, 64 is the required number.

10. Raj travels 360 km on three-fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol?

Distance travelled by Raj with three-fifths (i.e. ⅗) of petrol tank = 360 km

Distance travelled by him with a full petrol tank = (360 ÷ 3/5) km

= (360 x 5)/3 km

= 120 x 5 km

Video Lesson on Fractions

Practice Questions on Fractions

1. The weight of an object on the moon is 1/6 its weight on the Earth. If an object weighs 5 3/5 kg on the Earth, how much would it weigh on the moon?

2. Lipika reads a book for 1 ¾ hour every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

3. Multiply and reduce to the lowest form (if possible).

• 11/2 × 3/10

4.  Arrange the following in descending order:

• 2/9, 2/3, 8/21
• 1/5, 3/7, 7/10

5. Write five equivalent fractions of 8/11.

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Algebra: Fraction Problems

Related Topics: More Algebra Word Problems

In these lessons, we will learn how to solve fraction word problems that deal with fractions and algebra. Remember to read the question carefully to determine the numerator and denominator of the fraction.

We will also learn how to solve word problems that involve comparing fractions, adding mixed numbers, subtracting mixed numbers, multiplying fractions and dividing fractions.

Fraction Word Problems using Algebra

Example: 2/3 of a number is 14. What is the number?

Answer: The number is 21.

Example: The numerator of a fraction is 3 less than the denominator. When both the numerator and denominator are increased by 4, the fraction is increased by fraction.

Solution: Let the numerator be x, then the denominator is x + 3, and the fraction is \(\frac{x}{{x + 3}}\) When the numerator and denominator are increased by 4, the fraction is \(\frac{{x + 4}}{{x + 7}}\) \(\frac{{x + 4}}{{x + 7}} - \frac{x}{{x + 3}} = \frac{{12}}{{77}}\) 77(x + 4)(x + 3) – 77x(x+7) = 12(x + 7)(x + 3) 77x 2 + 539x + 924 – 77x 2 – 539x = 12x 2 + 120x + 252 12x 2 + 120x – 672 = 0 x 2 + 10x – 56 = 0 (x – 4)(x + 14) = 0 x = 4 (negative answer not applicable in this case)

How to solve Fraction Word Problems using Algebra? Examples: (1) The denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is 1/3. Find the original fraction. (2) If 3 is subtracted from the numerator of a fraction, the value of the resulting fraction is 1/2. If 13 is added to the denominator of the original fraction, the value of the new fraction is 1/3. Find the original fraction. (3) A fraction has a value of 3/4. When 14 is added to the numerator, the resulting fraction has a value equal to the reciprocal of the original fraction, Find the original fraction.

Algebra Word Problems with Fractional Equations Solving a fraction equation that appears in a word problem Example: One third of a number is 6 more than one fourth of the number. Find the number.

Fraction and Decimal Word Problems How to solve algebra word problems with fractions and decimals? Examples: (1) If 1/2 of the cards had been sold and there were 172 cards left, how many cards were printed? (2) Only 1/3 of the university students wanted to become teachers. If 3,360 did not wan to become teachers, how many university were there? (3) Rodney guessed the total was 34.71, but this was 8.9 times the total. What was the total?

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Solving Problems with the Unknown in any position

Beginning as early as 1st grade, students should have experience solving addition and subtraction problems with the unknown in any position . Traditionally, we have tended to focus on result unknown problems, such as 3 + 2 = ⬜. But students also need to be able to solve problems such as 3 + ⬜ = 5. So exactly how do we go about building that understanding?

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number bonds

Flexibility with numbers begins in Kindergarten when students learn all the combinations for the numbers through 10. These combinations are often referred to as number bonds . Here you see a common way to show number bond relationships. In this case, you see all the ways to make 5.

You may notice that number bonds look a lot like fact families, and they are similar. The difference is how we approach building an understanding of the relationship between the numbers. When we taught fact families, it was typically done as a rote skill. Students knew that they needed to have two addition equations and two subtraction equations using the same numbers, yet they didn’t have an understanding of what the equations represented. We knew that because we would often see unreasonable results, like 2 – 5 = 3.

Students in Kindergarten need to first work with number bonds in a totally concrete way. You can find lots of different games, many with free downloads, in this post .

We can use number bond cards to help students understand the part/whole relationship of the numbers that make up a number bond. We want to start out with result unknown cards and provide students the concrete support of counters.

Here we see that they start out by putting teddy bear counters on the two parts that are known—3 bears on one part and 2 on the other. Next, students move the bears representing the two parts to the unknown whole section, finding that the whole is 5.

After lots of practice with result unknown , students can move to working with the cards with the unknown as one of the parts. Keep in mind that this won’t happen at the same time for all children. Differentiation is critical. We begin by placing the 5 bears on the whole. Next, we move 2 of the bears to the part we know. Finally the remaining 3 bears are moved to the unknown part. Be sure to provide plenty of guided practice during small group instruction before asking students to work with part unknown cards independently.

3 reads protocol

Using word problems makes abstract concepts more concrete because they put the numbers in a familiar context. However, we need to make sure that we help students develop reading comprehension skills to allow them to understand what the numbers represent in the context of the story. Enter a powerful strategy called the 3 Read Protocol.

The Three Reads Protocol, not surprisingly, involves reading a word problem three times, with each read having a different purpose.

But here are some things that might surprise you.

The problem in Read 1 has NO numbers and NO question. When you take out the numbers, students have to focus on the words. This helps them learn to make mental pictures of what’s taking place, which helps them understand what math to do.

Read 2 provides the numbers, but still does not have a question. Now the focus shifts to the numbers and what they represent in the story.

Finally, in Read 3, students come up with questions that could complete the word problem.

While this sample problem is a result unknown problem (but could also be a comparison problem, right?), you would gradually introduce stories that have the unknown in other positions.

For more information on 3 Reads and how to incorporate it into your instructional routine, check out this post .

Part/whole models

Another tool that can be used to help students understand that the unknown can be in any position is a part/whole diagram. To illustrate, let’s revisit the word problem from the last section, but now let’s make at a part unknown problem.

Now let’s listen in on what it would sound like to incorporate part/whole thinking.

TEACHER: [displays the word problem and a blank part/whole diagram] Let’s read this problem together and decide how each number fits into our part/whole diagram. First we’ll read the whole problem and talk about what’s happening in this story. Then we’ll read each sentence and add the numbers to our diagram. [teacher and students read the story]

TEACHER: Who is this story about? [Juliet and her grandmother] What’s happening in the story? [Juliet is saving money for a video game. She already has some money. Her grandmother gives her money for her birthday.]

TEACHER: Okay, let’s go back to the first sentence:  Juliet has saved $15 for a video game.  Is the $15 she had already saved the whole, her total money, or is it part of her money. [part of her money] What part is it? [the part she had already saved] Great! Let’s add that to our part/whole diagram and label it money she had . Sound good?

TEACHER: Next sentence:  Her grandmother gave her some  [teacher shrugs her shoulders when she says some ] money for her birthday. Huh, do we know how much her grandmother gave her? [no] So that is our unknown in this problem! Is the money her grandmother gave her part of her money or all of the money, the total? [part] Can we label that part  money her grandmother gave her?  If we don’t have a number for the money her grandmother gave her, what should we put in that part of our diagram? [a question mark]

TEACHER: Next sentence:  Now she has $33. Is that all of her money, the whole, or one of the parts? [all of her money] Why don’t we label the whole All of her money  and add the $33 to our diagram.

TEACHER: It seem like we’re getting really close to solving this problem! Let’s read the question and make sure it matches where we placed the unknown in our diagram:  How much money did her grandmother give her? Does that match our diagram? [yes] Yes, because we have our question mark in the part labeled money her grandmother gave her .

TEACHER: Great work! Now work with your partner to solve the problem.

Let me add an important note—I used a missing part problem for this example. Keep in mind that your students would have been using the part/whole diagram and this process for talking through the problem on less complicated, result unknown problems extensively before moving on to unknown parts.

Another note—be careful of calling this a subtraction problem. Yes, most students will use subtraction to solve the problem, but they could also use a counting up strategy ( 18 and 2 more is 20. It’s 10 more to 30, and another 3 to 33. So her grandmother gave her $15 ). Allow for flexible strategies in solving ALL problems!

I hope that gives you some fresh ideas for tackling this tricky concept!

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Math Worksheets 3-5 Grade | 266 Word Problems | Addition | Subtraction | Multiplication | Division

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Math Worksheets 3th to 5th Grade | 266 Word Problems | Addition | Subtraction | Multiplication | Division | Instant Download | PRINTABLE PDF

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Dive into a world of numbers with our “Math Magic Worksheets Bundle”! Inspired by the need for engaging and practical math practice, this collection of 266 word problems has been meticulously crafted to challenge and delight students in 3rd to 5th grade. Imagine the satisfaction of solving puzzles that not only make math fun but also help build essential arithmetic skills.

Each worksheet is a labor of love, designed by educators who understand the importance of solid math foundations. From the first draft to the final polished product, we focused on creating problems that are not only educational but also intriguing for young minds.

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What is JUMP Math, and why are some teachers raving about it? Try 13 of its brain-teasing problems to find out

Michelle Jones says her students have been far more engaged since she started using the JUMP Math method at Jarvis Traditional Elementary School in Delta, B.C. Try the quiz at the end of this article to see whether you could solve the problems that Ms. Jones's Grade 6 students are expected to handle. Jennifer Gauthier/The Globe and Mail

In her more than two decades in front of a classroom, Michelle Jones has used five different math textbooks and, until recently, had grown increasingly frustrated in her inability to reach many of her students.

The story-based math problems that filled those textbooks left most of the children either checked out or confused. She’d draw on videos and other materials to supplement her lessons, but it didn’t feel like that was enough to help her students build their confidence in the subject.

Then, three years ago, her board – the Delta School District in Delta, B.C. – piloted a program that incorporated JUMP Math, a resource originally developed by John Mighton, an accomplished playwright and entrepreneur in Toronto. The program, run by a charity established in 2002, emphasizes students rehearsing basic arithmetic operations so they can see patterns and break problems down into smaller parts, gradually raising the level of difficulty. “We were just ready for a shift, to try something different,” said Ms. Jones, who teaches Grades 6 and 7 at Delta’s Jarvis Traditional Elementary School.

John Mighton helps Grade 4 pupils practice JUMP techniques at a Toronto school in 2007, five years after he developed the method. Deborah Baic/The Globe and Mail

For Ms. Jones, using JUMP Math – JUMP stands for Junior Undiscovered Math Prodigies – represented a sea change.

She is now armed with new strategies to teach the subject and has been able to reintroduce some rote learning so that students can engage with the material more quickly. The students use whiteboards, check in with their partners and practise on their own. As a result, she’s noticed they are less anxious and take more risks in class.

“In my experience, I have never seen students so engaged, relaxed and enjoying a math lesson,” she said.

The pilot at Delta has since expanded: In 14 of the district’s 24 elementary schools, most of the teachers are now using JUMP.

Focusing on math fact fluency may seem like an obvious recipe for success, but the way math is taught in schools has been the subject of a long-standing and divisive debate, much like reading.

On one side, some experts and educators believe rote learning creates anxiety and dread, and that children should approach the subject with playfulness and curiosity by learning through problem solving, pattern discovery and open-ended exploration.

Others have advocated for a so-called back-to-basics approach and pushed governments to initiate curriculum changes so students have the ability to quickly recall addition, subtraction, multiplication and division through repetition and memorization. Rote learning shouldn’t be considered a dirty phrase, they argue.

The debate comes at a critical time: Although Canada performs well compared with other countries globally, Canadian students’ scores on an international test administered by the Organization for Economic Co-operation and Development have been slipping for almost two decades – and the latest results from late last year show that slide continuing.

Neil Stephenson, director of learning services at Delta, brought in JUMP Math because he felt something needed to change in his district.

Educators were doing a “hodgepodge of things” to help students meet curriculum expectations, he said, which put an incredible strain on them to find and build lesson plans.

After doing some research and finding JUMP, he approached an elementary school that hadn’t been scoring well on provincial tests to see if any teachers there would try the program. Around three-quarters of them raised their hands – and assessments at the end of that school year showed that several students had progressed multiple grade-levels, and teacher confidence in how they approach the subject rose, he said.

“Absolutely we want kids to be doing creative work and solving interesting questions and synthesizing their knowledge. But there has to be some building up of that knowledge somewhere else first,” Mr. Stephenson said.

In Jarvis Elementary's district, more than half the schools now use JUMP for math education. Jennifer Gauthier/The Globe and Mail

That is heartening to JUMP’s founder.

Mr. Mighton didn’t fare well in math in school and nearly failed first-year calculus in university. But he slowly overcame his own math anxiety and, as a playwright trying to make a living, started tutoring the subject later in life. Teaching children encouraged him to break down difficult concepts into smaller parts, and, in turn, grasp the subject better. He relearned concepts he had missed along the way, and then returned to school in his early 30s to earn a PhD in math at the University of Toronto.

“Math is actually accessible, very accessible,” he said.

He explained that the current method – investigating ideas through problem solving, pattern discovery and open-ended exploration – rushes children past learning math facts in the hopes of making the subject more engaging. It has the opposite effect, he said, because children actually just become confused and disengaged.

His program provides lesson plans for teachers that allows for an incremental approach to problem solving. There’s a workbook for students, but Mr. Mighton said that should only be used after the lessons. “You want to get to those problems, but that’s not where you start. That’s the mistake we’re making,” he said. “We always think kids are experts. And we give them problems that are designed for experts when they’re novice learners.”

Math professor Anna Stokke feels that methods of teaching introduced in the 1980s have done a 'disservice to children' in the decades since. John Woods/the Globe and Mail

Anna Stokke, a mathematics professor at the University of Winnipeg and a vocal proponent for schools to once again focus on fundamentals, said the change in how math was taught began in the late 1980s under the school of thought called constructivism. The theory suggests students should not passively acquire knowledge through direct instruction but rather learn through experiences and interactions. At the time, the National Council of Teachers of Mathematics in the U.S. released a set of standards where problem solving became the focus of instruction, she said. The movement then spread to Canada.

Prof. Stokke said the change in instruction has been a “disservice to children” because students should be practising math procedures and memorizing facts before they can grasp more complex problems. “I’m a mathematician and, believe me, I know how to solve complex problems. And you can’t do complex problems without having a web of knowledge in your brain.”

The result of this change has been a widening equity gap, she said, where families who have the means provide tutoring for their children, while others continue to struggle in the subject.

However, Jason To, a math co-ordinator at the Toronto District School Board, said the argument that schools are teaching one way over another is misplaced. He worries that some experts are latching onto international test scores and insinuating that inquiry-based instruction is dominating the education space. But teachers, he said, are doing both: instructing their students on math fluency and immersing them in complex problems.

“This debate to me is you got to do one versus the other, and it’s not productive. It’s more like, how do these co-exist?”

Math fluency, and the way it is measured in standardized test, can be polarizing subjects in the world of education. Justin Tang/The Globe and Mail

Janelle Feenan, a teacher and peer support co-ordinator at the Delta school division, echoed the sentiment. For years, she and her Grade 3 teacher colleague would spend an evening a week researching and pulling resources to help their students with math fluency and to develop a more comprehensive understanding for concepts.

“We were struggling a little bit to make sure our students were understanding what we were doing. We’re going through the motions, but we just didn’t feel that they were where they needed to be,” she said.

They raised their hands to participate in the pilot that introduced JUMP Math to students.

Having worked with the program, Ms. Feenan found that there’s a place for both the structural approach that JUMP provides as well as allowing for problem solving and conceptual understanding. She uses JUMP as her main lesson plan, and then supports that with games and visual aids to deepen understanding.

“Neither of those approaches alone would be adequate to prepare kids for success in math,” she said. “I think you have to supplement lessons with activities and resources that are fun and engaging to build their understanding and enrich their learning experience.”

Pop quiz: Test your math skills, JUMP-style

These are Grade 6-level problems from JUMP Math assessment and practice books. Get out your calculator app and give them a try!

c. If the pitcher pitches on the first game (or on the second, or on the third), she will pitch a total of 10 games, ending on the 46th game (or 47th, or 48th, respectively).

Photo: Jon Blacker/The Canadian Press

d. The lake with the longest shoreline is Huron, at 6,164 km. The shortest is Lake Ontario, 1,146 km. The difference is 6,164 – 1,146 = 5,018 km.

a. Avril’s grade sold 10 + 15 + 25 + 10 = 60 tickets in total. Of those 60 tickets, 30 (half) are adult tickets and sell for $5 each, and the other 30 sell for $3 each. So Avril’s grade raises (30 × $5) + (30 × $3) = $150 + $90 = $240. Since the bus costs $320, there is still $320 – $240 = $80 needed.

c. Round 3,128 to 3,000, and 4,956 to 5,000. So 3,128 × 4,956 is approximately equal to 3,000 × 5,000 = 15,000,000, i.e., 15 million.

b. 821 × 4 = 3,284. To calculate mentally, multiply the digits separately.

c. The perimeter of the field is 921 × 5 = 4,605 m. The farmer needs 4,605 – 4,500 = 105 more metres of fence to surround the field.

Photo illustration (source: Ina Fassbender/AFP/Getty Images, JUMP Math

b. Add the digits and check if the sum makes a multiple of nine.

c. 40 per cent of 20 = 8, and 25 per cent of 20 = 5. Since 8 + 5 = 13, there are 20 – 13 = 7 green fish.

a. $7.21 × 3 = $21.63. To multiply mentally, multiply the digits separately.

Photo: Kham/Reuters

d. 84.8 mm ÷ 4 = 21.2 mm. To divide mentally, divide the digits separately.

b. 220 kg ÷ 4 = 55 kg.

c. 15 × 8 = 120, 120 ÷ 100 = 1.20. They will pay $1.20 in taxes.

d. Three quarters of 12 is nine, so nine green balloons have writing on them. Sixty per cent of 15 is nine, so nine blue balloons have writing on them. So, 9 + 9 = 18 balloons in total have writing on them.

Photo: Vadim Ghirda/AP

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