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Addition and Subtraction of Similar Fractions

Addition and subtraction of similar fractions is nothing but the usual arithmetic operation. After identifying that all denominators were the same, the rest will just be an ordinary addition or subtraction of our numerators. The denominators will tell us if we can add or subtract them directly.

If we are dealing with denominators, this means that we are dealing with both similar fractions (also called as like fractions) and dissimilar fractions (or unlike fractions). I have already discussed similar and dissimilar fraction in my previous post. For those who want to review, check my post entitled “Types of Fractions” .

In this lesson, I will be presenting the basic procedure (step-by-step) on how to add or subtract similar fractions. It will be followed by various examples for you to understand it better.

How to Add Similar Fractions (the same denominators)

As a review, similar fractions (also like fractions) are fractions having the same denominators.

The following are the steps on how to add similar fractions:

Step 1: Ensure that all denominators are the same.

Step 2: Add all the numerators. The sum will be the numerator of our answer.

Step 3: Copy the denominator. This will be the denominator of our answer.

Step 4. Add all the whole numbers if it is mixed numbers.

Step 5. Convert your answer into its lowest term or mixed numbers.

Do you want examples? We will be giving you various examples for you to understand it better.

Adding Similar Fractions Examples:

Example no.1  This is how we add proper fractions with the same denominators.

Solve 1/5 +3/5.

Step 1 is to check the denominators. All the denominators are the same 5 thus we can proceed to step 2.

Step 2 is to add all the numerators. Let us add 1 and 3. This will give us 4.

Step 3 is to copy the denominator. Our denominator is 5.

Step 4 is to add whole numbers. Since we do not have mixed numbers, then we can skip this step.

Step 5 is to convert our answer into its lowest term. Since 4/5 is already the lowest term, then 4/5 is our final answer.

Example no.2 Let us try to add more proper fractions.

Example no. 3 Let’s have another example.

Example no. 4  The same procedure will be applied when adding improper fractions with the same denominator.

Example no. 5  Let’s take a look at another example of adding similar fractions. This time, we are going to add a proper fraction and an improper fraction. We will follow the same steps.

Example no. 6  This time, let us add mixed numbers. The easiest way to add mixed numbers is to add them according to our procedure. Add the proper fractions and then the whole numbers. See the following example.

Example no. 7  However, there are some problems in which after adding proper fractions, the result will be an improper fraction. Mixed numbers must have only a whole number and a proper fraction. If the partner of your whole number is an improper fraction, then you need to convert the improper fraction into mixed numbers and combine the whole numbers. See the example below.

Note: 7/5 is not a proper fraction. A mixed number should have only a proper fraction and a whole number. Therefore, we need to convert it into a mixed number.

In this problem, it is better to convert the mixed numbers into an improper fraction and do the addition according to our procedure to avoid confusion. Let us solve example no.7 again.

For me, this is way more easy than the previous one. But, whatever technique you are comfortable to use with, it will still give you the correct answer.

Example no. 8  We can also add a mixed number and a proper fraction. The procedure is the same as example no.6.

If the result after adding the proper fractions is more than one, then follow the procedure in example no.7. Let us see another example.

Example no. 9  How about adding mixed numbers and improper fractions?

Example no.10  Now, let us add similar fractions of different types.

How to Subtract Similar Fractions

Dealing with the addition of similar fraction is quite simple. You just have to ensure that the denominators are the same so that you can proceed to add the numerators.

Subtracting similar fractions have the same procedure with adding similar fractions. The only difference is that you will be dealing with subtraction.

Let’s start.

Subtracting Similar Fractions Examples:

Example no.11  Subtracting proper fractions with the same denominators.

Observe that we just follow the same procedure as the addition of fractions with the same denominators.

Example no.12  We can have also negative fractions as our results. Negative fractions are fractions which are less than zero.

Example no.13  Subtracting improper fractions with the same denominators.

Example no.14  In this example, we will subtract mixed numbers of similar fractions. It will be easy if we will convert mixed numbers into improper fractions and proceed with our procedure.

Example no.15 More examples subtracting similar fractions.

Summary of Adding and Subtracting Fractions

1. To add or subtract similar fractions, just add or subtract all the numerators and copy the denominators. Then, convert the answer to lowest term or mixed number.

2. For adding or subtracting mixed numbers with similar denominators, first, convert mixed numbers into improper fractions. Then, add or subtract the numerators and just copy the denominators. Convert your answer to lowest term or mixed number.

Related Topics

1. What is a fraction?

2. Types of Fractions.

3.  What are similar fractions or like fractions?

4. What are dissimilar fractions or unlike fractions?

5. What are Equivalent Fractions?

6.  How to Simplify Fractions?

7. How to convert an improper fraction into a mixed number?

8.  How to convert a mixed number into an improper fraction?

If you have some questions or problems related to the above topic, please feel free to drop those in the comments section below. You can also send your concerns to our support team at [email protected].

The math-lover.com is happy to have you here reading this post.

Adding and Subtracting numbers is time consuming and can exhaust too much energy on thinking what is the right answer. If practicing how to add and subtract numbers, it is better to do it manually but when you are in an actual situation that you are doing arithmetic operation, it is better to use calculator. Using calculator is not bad and it is a good strategy to save your time and physical strength plus you can be sure that you got the correct answer.

Masarap basahin Ito dahil marami Kang natutuhan sa subtract at sa iba ang math.

I want to learn math.

I learned about it.

Thank you ju.

pls an appropriate methods to teach the grade 7 pls help with illustrations

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Adding Fractions with Like Denominators

Welcome to our Adding Fractions with Like Denominators page.

Here you will find our selection of worksheets designed to help your child master the skill of adding fractions with the same denominator.

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Adding fractions with like denominators worksheets.

• Adding Subtracting Fractions with Like Denominators Worksheets
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How to Add and Subtract Fractions Support

Here you will find support pages about how to add and subtract fractions (with both like and unlike denominators).

• How do you add Fractions?
• Steps to subtract Fractions?

How to Add and Subtract Fractions with Like Denominators Video

Find out how to add and subtract fractions with like denominators using the video below.

If you want to use our Free Fraction Calculator to do the work for you then use the link below.

Our Fraction calculator will allow you to add or subtract fractions and show you the steps to work it out.

Otherwise, for more detailed support and worksheets, keep reading!

• Free Fraction Calculator

Here you will find a selection of Free Fraction worksheets designed to help your child understand how to add fractions with the same denominator. The sheets are graded so that the easier ones are at the top.

Using these sheets will help your child to:

• add (and subtract) fractions with the same denominator.
• solve a problem where the answer is given and one of the addends is missing.

We have split the worksheets into 3 sections:

• The first section contains adding fractions using circles - a visual way to understand this concept.
• The second section contains just adding fractions with like denominators with no extra support.
• The third section contains both adding and subtracting fractions with like denominators.

Adding Fractions with Like Denominators Using Circles

A great way to introduce and understand this concept is to use visual representations of fractions.

The questions on these sheets involve shading different fractions and then working out the total fraction shaded.

This is then converted into a simple fraction addition sentence!

• Adding Fractions With Like Denominators Using Circles 1
• PDF version
• Adding Fractions With Like Denominators Using Circles 2
• Adding Fractions With Like Denominators Using Circles 3

Adding Fractions with Like Denominators - problems only

• Adding Fractions With Like Denominators 1
• Adding Fractions With Like Denominators 2
• Adding Fractions With Like Denominators 3

Adding & Subtracting Fractions with Like Denominators

The first sheet involves using fraction diagrams to look at the pattern between adding and subtracting fractions.

The other 3 sheets are more traditional fraction problems involving adding and subtracting fractions.

• Adding Subtracting Fractions Like Denominators Using Circles 1
• Adding Subtracting Fractions like denominators 1
• Adding Subtracting Fractions like denominators 2
• Adding Subtracting Fractions like denominators 3

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

• Subtracting Fractions with like denominators

We also have a selection of worksheets involving subtracting fractions with like denominators.

These sheets are similar to the ones on this page, but involve subtraction instead of addition.

Adding & Subtracting Fractions with unlike denominators

These sheets are all about adding (and subtracting) fractions with different denominators.

• add and subtracting fractions with different denominators;
• apply your equivalent fractions knowledge.
• Adding Fractions Worksheets with unlike denominators
• Adding Subtracting Fractions with unlike denominators
• Fractions Adding and Subtracting Worksheets (randomly generated)

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5.1: Addition and Subtraction of Fractions with Like Denominators

• Last updated
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• Page ID 48857

• Denny Burzynski & Wade Ellis, Jr.
• College of Southern Nevada via OpenStax CNX

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Learning Objectives

• be able to add and subtract fractions with like denominators

Addition of Fraction With Like Denominators

Let's examine the following diagram.

2 one-fifths and 1 one fifth is shaded.

It is shown in the shaded regions of the diagram that

(2 one-fifths) + (1 one-fifth) = (3 one-fifths)

\(\dfrac{2}{5} + \dfrac{1}{5} = \dfrac{3}{5}\)

From this observation, we can suggest the following rule.

Method of Adding Fractions Having Like Denominators To add two or more fractions that have the same denominators, add the numer­ators and place the resulting sum over the common denominator. Reduce, if necessary.

Sample Set A

Find the following sums.

\(\dfrac{3}{7} + \dfrac{2}{7}\). The denominators are the same. Add the numerators and place that sum over 7.

\(\dfrac{3}{7} + \dfrac{2}{7} = \dfrac{3 + 2}{7} = \dfrac{5}{7}\)

\(\dfrac{1}{8} + \dfrac{3}{8}\). The denominators are the same. Add the numerators and place the sum over 8. Reduce.

\(\dfrac{1}{8} + \dfrac{3}{8} = \dfrac{1 + 3}{8} = \dfrac{4}{8} = \dfrac{1}{2}\)

\(\dfrac{4}{9} + \dfrac{5}{9}\). The denominators are the same. Add the numerators and place the sum over 9.

\(\dfrac{4}{9} + \dfrac{5}{9} = \dfrac{4 + 5}{9} = \dfrac{9}{9} = 1\)

\(\dfrac{7}{8} + \dfrac{5}{8}\). The denominators are the same. Add the numerators and place the sum over 8.

\(\dfrac{7}{8} + \dfrac{5}{8} = \dfrac{7 + 5}{8} = \dfrac{12}{8} = \dfrac{3}{2}\)

To see what happens if we mistakenly add the denominators as well as the numerators, let's add

\(\dfrac{1}{2} + \dfrac{1}{2}\)

Adding the numerators and mistakenly adding the denominators produces

\(\dfrac{1}{2} + \dfrac{1}{2} = \dfrac{1 + 1}{2 + 2} = \dfrac{2}{4} = \dfrac{1}{2}\)

This means that two \(\dfrac{1}{2}\)'s is the same as one \(\dfrac{1}{2}\). Preposterous! We do not add denominators .

Practice Set A

\(\dfrac{1}{10} + \dfrac{3}{10}\)

\(\dfrac{2}{5}\)

\(\dfrac{1}{4} + \dfrac{1}{4}\)

\(\dfrac{1}{2}\)

\(\dfrac{7}{11} + \dfrac{4}{11}\)

\(\dfrac{3}{5} + \dfrac{1}{5}\)

\(\dfrac{4}{5}\)

Show why adding both the numerators and denominators is preposterous by adding \(\dfrac{3}{4}\) and \(\dfrac{3}{4}\) and examining the result.

\(\dfrac{3}{4} + \dfrac{3}{4} = \dfrac{3 + 3}{4 + 4} = \dfrac{6}{8} = \dfrac{3}{4}\), so two \(\dfrac{3}{4}\)'s = one \(\dfrac{3}{4}\), whihch is preposterous.

Subtraction of Fractions With Like Denominators

We can picture the concept of subtraction of fractions in much the same way we pictured addition.

From this observation, we can suggest the following rule for subtracting fractions having like denominators:

Subtraction of Fractions with Like Denominators To subtract two fractions that have like denominators, subtract the numerators and place the resulting difference over the common denominator. Reduce, if possible.

Sample Set B

Find the following differences.

\(\dfrac{3}{5} - \dfrac{1}{5}\). The denominators are the same. Subtract the numerators. Place the difference over 5.

\(\dfrac{3}{5} - \dfrac{1}{5} = \dfrac{3 - 1}{5} = \dfrac{2}{5}\)

\(\dfrac{8}{6} - \dfrac{2}{6}\). The denominators are the same. Subtract the numerators. Place the difference over 6.

\(\dfrac{8}{6} - \dfrac{2}{6} = \dfrac{8 - 2}{6} = \dfrac{6}{6} = 1\)

\(\dfrac{16}{9} - \dfrac{2}{9}\). The denominators are the same. Subtract numerators and place the difference over 9.

\(\dfrac{16}{9} - \dfrac{2}{9} = \dfrac{16 - 2}{9} = \dfrac{14}{9}\)

To see what happens if we mistakenly subtract the denominators, let's consider

\(\dfrac{7}{15} - \dfrac{4}{15} = \dfrac{7 - 4}{15 - 15} = \dfrac{3}{0}\)

We get division by zero, which is undefined. We do not subtract denominators.

Practice Set B

\(\dfrac{10}{13} - \dfrac{8}{13}\)

\(\dfrac{2}{13}\)

\(\dfrac{5}{12} - \dfrac{1}{12}\)

\(\dfrac{1}{3}\)

\(\dfrac{1}{2} - \dfrac{1}{2}\)

\(\dfrac{26}{10} - \dfrac{14}{10}\)

\(\dfrac{6}{5}\)

Show why subtracting both the numerators and the denominators is in error by performing the subtraction \(\dfrac{5}{9} - \dfrac{2}{9}\)

\(\dfrac{5}{9} - \dfrac{2}{9} = \dfrac{5 - 2}{9 - 9} = \dfrac{3}{0}\), which is undefined

For the following problems, find the sums and differences. Be sure to reduce.

Exercise \(\PageIndex{1}\)

\(\dfrac{3}{8} + \dfrac{2}{8}\)

\(\dfrac{5}{8}\)

Exercise \(\PageIndex{2}\)

\(\dfrac{1}{6} + \dfrac{2}{6}\)

Exercise \(\PageIndex{3}\)

\(\dfrac{9}{10} + \dfrac{1}{10}\)

Exercise \(\PageIndex{4}\)

\(\dfrac{3}{11} + \dfrac{4}{11}\)

Exercise \(\PageIndex{5}\)

\(\dfrac{9}{15} + \dfrac{4}{15}\)

\(\dfrac{13}{15}\)

Exercise \(\PageIndex{6}\)

\(\dfrac{3}{10} + \dfrac{2}{10}\)

Exercise \(\PageIndex{7}\)

\(\dfrac{5}{12} + \dfrac{7}{12}\)

Exercise \(\PageIndex{8}\)

\(\dfrac{11}{16} - \dfrac{2}{16}\)

Exercise \(\PageIndex{9}\)

\(\dfrac{3}{16} - \dfrac{3}{16}\)

Exercise \(\PageIndex{10}\)

\(\dfrac{15}{23} - \dfrac{2}{23}\)

Exercise \(\PageIndex{11}\)

\(\dfrac{1}{6} - \dfrac{1}{6}\)

Exercise \(\PageIndex{12}\)

\(\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4}\)

Exercise \(\PageIndex{13}\)

\(\dfrac{3}{11} + \dfrac{1}{11} + \dfrac{5}{11}\)

\(\dfrac{9}{11}\)

Exercise \(\PageIndex{14}\)

\(\dfrac{16}{20} + \dfrac{1}{20} + \dfrac{2}{20}\)

Exercise \(\PageIndex{15}\)

\(\dfrac{12}{8} + \dfrac{2}{8} - \dfrac{1}{8}\)

Exercise \(\PageIndex{16}\)

\(\dfrac{11}{16} + \dfrac{9}{16} - \dfrac{5}{16}\)

Exercise \(\PageIndex{17}\)

\(\dfrac{4}{20} - \dfrac{1}{20} + \dfrac{9}{20}\)

\(\dfrac{3}{5}\)

Exercise \(\PageIndex{18}\)

\(\dfrac{7}{10} - \dfrac{3}{10} + \dfrac{11}{10}\)

Exercise \(\PageIndex{19}\)

\(\dfrac{16}{5} - \dfrac{1}{5} - \dfrac{2}{5}\)

\(\dfrac{13}{5}\)

Exercise \(\PageIndex{20}\)

\(\dfrac{21}{35} - \dfrac{17}{35} + \dfrac{31}{35}\)

Exercise \(\PageIndex{21}\)

\(\dfrac{5}{2} + \dfrac{16}{2} - \dfrac{1}{2}\)

Exercise \(\PageIndex{22}\)

\(\dfrac{1}{18} + \dfrac{3}{18} + \dfrac{1}{18} + \dfrac{4}{18} - \dfrac{5}{18}\)

Exercise \(\PageIndex{23}\)

\(\dfrac{6}{22} - \dfrac{2}{22} + \dfrac{4}{22} - \dfrac{1}{22} + \dfrac{11}{22}\)

The following rule for addition and subtraction of two fractions is preposterous. Show why by performing the operations using the rule for the following two problems.

Preposterous Rule To add or subtract two fractions, simply add or subtract the numerators and place this result over the sum or difference of the denominators.

Exercise \(\PageIndex{24}\)

\(\dfrac{3}{10} - \dfrac{3}{10}\)

Exercise \(\PageIndex{25}\)

\(\dfrac{8}{15} + \dfrac{8}{15}\)

\(\dfrac{16}{30} = \dfrac{8}{15}\) (using the preposterous rule)

Exercise \(\PageIndex{26}\)

Find the total length of the screw.

Two months ago, a woman paid off \(\dfrac{3}{24}\) of a loan. One month ago, she paid off \(\dfrac{5}{24}\) of the total loan. This month she will again pay off \(\dfrac{5}{24}\) of the total loan. At the end of the month, how much of her total loan will she have paid off?

\(\dfrac{13}{24}\)

Exercise \(\PageIndex{27}\)

Find the inside diameter of the pipe.

Exercises for Review

Exercise \(\PageIndex{28}\)

Round 2,650 to the nearest hundred.

Exercise \(\PageIndex{29}\)

Use the numbers 2, 4, and 8 to illustrate the associative property of addition.

Exercise \(\PageIndex{30}\)

Find the prime factors of 495.

\(3^2 \cdot 5 \cdot 11\)

Exercise \(\PageIndex{31}\)

Find the value of \(\dfrac{3}{4} \cdot \dfrac{16}{25} \cdot \dfrac{5}{9}\).

Exercise \(\PageIndex{32}\)

\(\dfrac{8}{3}\) of what number is \(1 \dfrac{7}{9}\)?

\(\dfrac{2}{3}\)

• Math Article

Addition of Fractions

The addition of fractions teaches us to add two or more fractions with the same or different denominators. The addition  of fraction depends  on two major conditions: 

• Same denominators
• Different denominators

While adding fractions, if denominators are the same (such fractions are said to be like fractions), then they can be added directly. But if the denominators are different, (such fractions are called unlike fractions) then we need to make the denominators same and then add the fractions. Learn  like or unlike fractions , here.

Addition of Fractions with Same Denominators

If denominators of two or more fractions are same, then we can directly add the numerators, keeping the denominator common. 

Follow the below steps to add the fractions with same denominators:

• Add the numerators together, keeping the denominator common
• Write the simplified fraction

For example: Add the fractions: 5/6 and 7/6.

Since the denominators are same, therefore we can add the numerators directly.

(5/6) + (7/6) = (5 + 7)/6 = 12/6

• Simplify the fraction

Hence, the sum of ⅚ and 7/6 is 2.

Adding fractions with Different Denominators

When two or more fractions with different denominators are added together, then we cannot the numerators directly. 

Follow the below steps to add fractions with different denominators:

• Check the denominators of the fractions.
• Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them
• Add the numerators of the fractions, keeping the denominator common
• Simplify the fraction to get final sum

For example: Add 3/12 + 5/2

Solution: Both the fractions 3/12 and 5/2 have different denominators.

We can write 3/12 = ¼, in a simplified fraction.

Now, ¼ and 5/2 are two fractions.

LCM of 2 and 4 = 4

Multiply 5/2 by 2/2.

5/2 x 2/2 = 10/4

Now add ¼ and 10/4

¼ + 10/4 = (1+10)/4 = 11/4

Hence, the sum of 3/12 and 5/2 is 11/4.

Adding fractions with whole numbers

Add the fraction and a whole number with three simple steps:

• Write the given whole number in the form of a fraction (for example, 3/1)
• Make the denominators same and add the fractions

For example: Add 7/2 + 4

Here, 7/2 is a fraction and 4 is a whole number.

We can write 4 as 4/1.

Now making the denominators same, we get;

7/2 and 4/1 x (2/2) = 8/2

Add 7/2 and 8/2

7/2 + 8/2 = 15/2

Hence, the sum of 7/2 and 4 is 15/2.

Adding Fractions with Co-prime Denominators

Co-prime  denominators : The denominators which do not have common factors, other than 1.

Let us learn how to add fractions with co-prime denominators with the help of the following steps:

• Check the denominators whether they are co-prime
• Multiply the first fraction (numerator and denominator) with the denominator of the other fraction and the second fraction (numerator and denominator) with the denominator of the first fraction.
• Add the resulting fractions and simplify

For example, the addition of fractions 9/7 and 3/4 can be done as follows.

The denominators 7 and 4 are coprime since they have only one highest common factor 1.

So, (9/7) + (3/4) = [(9 × 4) + (3 × 7)]/ (7 × 4)

= (36 + 21)/28

Adding Mixed Fractions

A mixed fraction is a combination of a whole number and a fraction. To add two mixed fractions, we need to convert them first into improper fractions and then add them together.

Follow the below steps to add mixed numbers:

• Convert the given mixed fraction into improper fractions
• Check if denominators are the same or different
• If different denominators, then rationalise them
• Add the fractions and simplify

Let’s understand how to add mixed fractions with an example:

Example: Add : 3 ⅓  + 1 ¾

Step1: Convert the given mixed fractions to improper fractions.

3 ⅓  = 10/3 

Step 2: Make the denominators same by taking the LCM and multiplying the suitables fractions for both.

LCM of 3 and 4 is 12.

So, 10/3 = (10/3) × (4/4) = 40/12

7/4 = (7/4) × (3/3) = 21/12

Step 3: Take the denominator as common and add numerators.  Then, write the final answer.

(40/12) + (21/12) = (40 + 21)/12 = 61/12      

Therefore, 3 ⅓  + 1 ¾ = 61/12 = 5 1/12

Subtraction of Fractions

As we know, addition and subtraction are similar operations in Maths. In addition, we add two or more numbers, whereas, in subtraction, we subtract a number from another. Therefore, subtraction of fractions also follows the same rule as addition of fractions. 

If the denominators are the same for given fractions, then we can directly subtract the numerator, keeping the denominator same.

If the denominators of fractions are different, we need to rationalise them first and then perform subtraction. 

Some examples are:

Example 1: Subtract ⅓ from 8/3.

Solution: We need to find,

8/3 – ⅓ = ?

Since the denominator of two fractions ⅓ and 8/3 is common, therefore, we can directly subtract them:

8/3 – ⅓ = (8-1)/3 = 7/3

Example 2: Subtract ½ from ¾. 

Solution: We need to subtract ½ from ¾, i.e.,

¾ – ½ = ?

Since the denominators of two fractions are different, therefore, we need to rationalise them by taking the LCM.

LCM (4,2) = 4

Now multiply the ½ by 2/2, to get 2/4

¾ – 2/4 = (3-2)/4 = ¼

Hence, ¾ – ½ = ¼

Video Lesson on Fractions

Solved Examples

Let us solve some problems based on adding fractions.

Q. 1: Add 1/2 and 7/2.

Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.

Q. 2: Add 3/5 and 4.

Solution: We can write 4 as 4/1

Now, 3/5 and 4/1 are the two fractions to be added.

Since the denominators here are different, thus we need to simplify the denominators first, before adding the fractions.

Taking LCM of 5 and 1, we get;

LCM(5,1) = 5

Therefore, multiplying the second fraction, 4/1 by 5 both in numerator and denominator, we get;

(4×5)/((1×5) = 20/5

Now 3/5 and 20/5 have a common denominator, i.e. 5, therefore, adding the fractions now;

Addition of Fraction Worksheet

Fraction addition is one of the important topics in classes 6, 7 and 8. We have provided a worksheet for the addition of fractions here. After practising the questions given in this worksheet, you’ll be able to solve ant fraction addition sums easily. Practice from the given addition of fraction worksheet link here and score well in exams.

Practice Questions

• 1(⅓) + 3(5/2) = 
• 2(¾) + ___ = 7
• 3/7 + 2 + 4/3 = ?

Related Articles

Frequently asked questions – faqs, how to add two fractions with different denominators, what are the rules to add and subtract fractions, how to add whole numbers and fractions, how to add large fractions, how to add fractions with like denominators.

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Fraction Addition Word Problems Worksheets

Let children work on our printable adding fractions word problems worksheets hammer and tongs! Whether it's sharing a meal with your friends or measuring the ingredients for a recipe, adding fractions is at the heart of it all, hence our worksheets. A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!

Adding Fractions with Whole Numbers

Dazzle 3rd grade kids with a gift of lifelike story problems! If you're a novice up against fraction addition, don't miss our pdf adding fractions word problems worksheets using whole numbers and fractions!

• Download the set

Adding Like Fractions Word Problems

Gerald ate 5/9 of an apple, and Garry ate 4/9 of it. How many apples did they eat in all? Good going! They both ate one whole apple. Simply combine the numerators and solve the like fraction word problems here!

Adding Unlike Fractions

A potpourri of word problems that involve adding unlike fractions, these pdfs mean that 4th grade and 5th grade students will breeze through addition of fractions with different denominators in their day-to-day lives.

Adding Mixed Numbers | Same Denominators

See in your mind's eye adding mixed numbers with same denominators riding on the several real-life scenarios in our printable worksheets! Convert the mixed numbers to fractions, and add them as usual.

Adding Mixed Numbers | Different Denominators

Steal a march on your 5th grade and 6th grade peers by getting your act together to power through the real-world situations featured in this set of printable adding mixed numbers word problems worksheets.

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» Adding Like Fractions

» Adding Unlike Fractions

» Adding Mixed Numbers

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Adding like fractions

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Here are some more fraction worksheets you can use in grade 4. They also use only fractions with a same denominator (like fractions).

Fraction addition worksheets: grade 5

In grade 5, students learn to add unlike fractions — fractions with different denominators.

Here are some more fraction worksheets for grade 5.

Fraction addition worksheets: grades 6-7

In grades 6 and 7, students simply practice addition with fractions that have larger denominators than in grade 5.

Fraction worksheets generator

Use the generator to make customized worksheets for fraction operations.

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Course: 5th grade   >   Unit 4

• Adding fractions with unlike denominators introduction
• Adding fractions with unlike denominators

Add fractions with unlike denominators

• Subtracting fractions with unlike denominators introduction
• Subtracting fractions with unlike denominators
• Adding and subtracting 3 fractions
• Solving for the missing fraction
• Add and subtract fractions

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs

What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.

Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:

• Addition and subtraction of like fractions (fractions with same denominators)
• Addition and subtraction of unlike fractions (fractions with different denominators)

A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.

Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.

Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators. 

When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.

Related Worksheets

Addition and Subtraction of Like Fractions

The rules for adding fractions with the same denominator are really simple and straightforward. 

Let’s learn with the help of examples and visual bar models.

Addition of Like Fractions

Here are the steps to add fractions with the same denominator:

Step 1: Add the numerators of the given fractions. 

Step 2: Keep the denominator the same. 

Step 3: Simplify.          

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$  …$c \neq 0$

Example 1: Find $\frac{1}{4} + \frac{2}{4}$ .

$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$

We can visualize this addition using a bar model:

Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$

Subtraction of Like Fractions

Here are the steps to subtract fractions with the same denominator:

Step 1: Subtract the numerators of the given fractions. 

Step 3: Simplify. 

$\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$

Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$.

$\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$

Addition and Subtraction of Unlike Fractions

Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!

Addition of Unlike Fractions

We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator. 

Example: $\frac{3}{5} + \frac{3}{2}$

Step 1: Find the LCM (Least Common Multiple) of the two denominators.

The LCM of 5 and 2 is 10.

Step 2: Convert both the fractions into like fractions by making the denominators same.  

$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$  

$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$

Step 3: Add the numerators. The denominator stays the same.

$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$

Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1. 

In this case, GCF (21,10) $= 1$

The fraction $\frac{21}{10}$ is already in its simplest form. 

Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$

Subtraction of Unlike Fractions

Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.

Example: $\frac{5}{6} \;-\; \frac{2}{9}$

Step 1: Find the LCM of the two denominators.

LCM of 6 and $9 = 18$

Step 2: Convert both the fractions into like fractions by making the denominators same.

$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$   

$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$

Step 3: Subtract the numerators. The denominator stays the same.

$\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$

In this case, the GCF (11,18) $= 1$

So, it is already in its simplest form. 

Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$

A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa. 

Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .

Addition and Subtraction of Mixed Fractions with Same Denominators

The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.

Step 1: Convert the given mixed fractions to improper fractions.

Step 2: Add/Subtract the like fractions obtained in step 1.

Step 3: Reduce the fraction to its simplest form.

Step 4: Convert the resulting fraction into a mixed number.

Example 1: $2\frac{1}{5} + 1\frac{3}{5}$

$2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$

$1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$

Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$

Converting $\frac{19}{5}$ into a mixed number, we get

$\frac{19}{5} = 3\frac{4}{5}$

Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$

Addition and Subtraction of Mixed Fractions with Unlike Denominators

Step 2: Convert both the fractions into like fractions by finding the least common denominator.

Step 3: Add the fractions. (or subtract the fractions.)

Step 4: Reduce the fraction if possible or convert back to a mixed number 

Let us understand the addition of mixed numbers with unlike denominators with the help of an example.

Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$.

Convert the given mixed fractions to improper fractions.

$1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$

Step 2: Convert both the fractions into like fractions by making the denominators the same.

Here, LCM of 5 and 2 is 10.

Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$

Step 3: Add the fractions by adding the numerators.

$\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$

Step 4: Convert back into a mixed number. 

Thus, $\frac{41}{10}$ will become  $4\frac{1}{10}$

Therefore, $1\frac{3}{5} + 2\frac{1}{2} =  4\frac{1}{10}$

Here’s an example for subtraction. It follows the same steps.

Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$

Step 1: Convert the mixed numbers into improper fractions.

     $6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$

Step 2: Make the denominators equal.

LCM of 2 and 4 is 4. 

   $\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$ 

Step 3: Subtract the fractions.

        $\frac{26}{4} \;-\;  \frac{7}{4} = \frac{19}{4}$

Step 4: Convert the fraction as a mixed number.

            $\frac{19}{4}  = 4\frac{3}{4}$  

Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4}  =   4\frac{3}{4}$  

Facts about Addition and Subtraction of Fractions

• We cannot add or subtract fractions without converting them into like fractions.
• Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators.
• Equivalent fractions are two different fractions that represent the same value.
• The LCD (least common denominator) of two fractions is the LCM of the denominators.

In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.

• Solve: $\frac{2}{4} + \frac{1}{4}$ .

Solution: 

Here, the denominators are the same.

Thus, we add the numerators by keeping the denominators as it is.

$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$ 

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.

$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.

The LCM of 2 and 5 is 10.

Thus, we can write

$\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$

$= \frac{6}{10} + \frac{25}{10}$

            $= \frac{6}{10} + \frac{25}{10}$

            $= \frac{31}{10}$

Thus, $\frac{3}{5} + \frac{5}{2} =  \frac{31}{10}$

3. Find $\frac{4}{16} + \frac{5}{8}$.

Solution:  

To add two fractions with different denominators, we first need to find the LCM of the denominators.

The LCM of 16 and 8 is 16.

$\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$ 

            $= \frac{10}{16} + \frac{4}{16}$ 

            $= \frac{14}{16}$

$= \frac{7}{8}$

4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope.

Total length of the rope $= 12\frac{1}{2}$ ft.

Length of the rope that was cut off $= 7 \frac{6}{8}$ ft. 

The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$

$12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$

         $= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$

         $= \frac{100}{8} \;-\; \frac{62}{8}$

         $= \frac{38}{8}$

         $= \frac{19}{4}$

Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.

Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.

Attend this quiz & Test your knowledge.

Find $\frac{2}{4} + \frac{2}{4}$.

$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.

How do we add and subtract negative fractions?

Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.

How can we convert an improper fraction into a mixed number?

To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.

Example: $\frac{14}{3} = 4\; \text{R}\; 2$

Quotient $= 4$

Remainder $= 2$

$\frac{14}{3} = 4\frac{2}{3}$

How do we divide two fractions?

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.

$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$

For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$

What are the rules of adding and subtracting fractions?

• Before adding or subtracting, we check if the fractions have the same denominator.
• If the denominators are equal, then we add/subtract the numerators keeping the common denominator.
• If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is.

How do we add and subtract fractions with whole numbers?

• Convert the whole number to a fraction. To do this, give the whole number a denominator of 1.
• Convert to fractions of like denominators. 
• Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem.

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Worksheet on Add and Subtract Fractions

Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtraction with the help of a fraction number line, add the fractions with the same denominator, subtract the fractions with the same denominator and word problems on add and subtract fractions.

1.  Add with the help of a fraction number line: (a) ²/₃ + ¹/₃

(b) ³/₇ + ²/₇

(c) ⁶/₁₀ + ¹/₁₀

2.  Subtract with the help of a fraction number line:  (a) ⁹/₁₀ - ³/₁₀

(b) ⁵/₆ - ²/₆

(c) ⁷/₈ - ⁴/₈

3. Add: 

(a) ⁷/₁₀ + ²/₁₀

(b) ⁶/₈ + ⁴/₈

(c) ⁵/₉ + ²/₉ + ¹/₉

(d) ⁸/₁₁ + ²/₁₁

(e) ⁴/₉ + ⁷/₉

(f) ³/₈ + ⁵/₈ + ²/₈

(g) ⁴/₆ + ²/₆ + ¹/₆

(h) ⁷/₁₂ + ⁵/₁₂ + ⁶/₁₂

4. Find the difference. Remember to show the answer in the simplest form: (a) ⁹/₁₄ - ⁴/₁₄

(b) ⁶/₁₁ - ³/₁₁

(c) ⁸/₁₂ - ⁴/₁₂

(d) ¹²/₁₅ - ⁹/₁₅

(e) ¹²/₁₃ - ⁹/₁₃

(f) ⁶/₁₀ - ²/₁₀

(g) ⁹/₁₆ - ⁵/₁₆

(h) ¹²/₁₄ - ⁸/₁₄

Worksheet on Word Problems on Addition and Subtraction of Like Fractions:

5. Solve these problems: (a) ¹/₃ of the school garden has vegetable and another ¹/₃ has flowers. What part of the garden is left to grow grass? (b) Sam spent ¹/₆ of his Sunday doing home work and ³/₆ of the day watching cricket. What part of the day was left to do other things? (c) My mother ate ¹/₈ of the cake and my father ³/⁸. How much of the cake has been eaten and how much is left? (d) Pearl bought ²/₃ of her school books last week. What part is still left to be bought? (e) Sonia walked ³/₈ of the distance to school and ran ⁵/₈ of the distance. How much more of the distance does she need to cover?

(f) Emma likes chocolate. One day she bought a chocolate and ate \(\frac{5}{8}\) of it in the morning and \(\frac{2}{8}\) in the evening. How much part of the chocolate has she eaten?

(g) James and  Lucas are eating a pizza.  James ate \(\frac{3}{4}\) of the pizza and  Lucas ate  \(\frac{1}{4}\) of pizza. Who ate more pizza?

(h) Sophia completed \(\frac{2}{5}\) of her homework before going out for play. She did \(\frac{1}{5}\) of her homework after the play. How much homework did she complete altogether?

(i) David distributed \(\frac{19}{24}\) apples in his class and gave \(\frac{2}{24}\) to his friend Richard. What fraction of apples he gave away in all?

(j) Mary read \(\frac{2}{9}\) of her book in the morning and \(\frac{5}{9}\) in the evening. What fraction of the book has she read?

(k) A piece of ribbon is \(\frac{12}{15}\) m long. A piece of \(\frac{4}{15}\) m is cut from it. What is the fraction of the remaining ribbon?

(l) Nancy saves \(\frac{2}{7}\) of her salary and uses \(\frac{1}{7}\) for paying the house rent. How much salary is she left with?

Answers for the worksheet on add and subtract fractions are given below to check the exact answers of the above questions on adding & subtracting fractions. 

●   Fractional Numbers - worksheets

Worksheet on Equivalent Fractions.

Worksheet on Fractions.

Worksheet on Comparison of Like Fractions.

Worksheet on Conversion of Fractions.

Worksheet on Changing Fractions.

Worksheet on Types of Fractions.

Worksheet on Reducing Fraction.

Worksheet on Addition of Fractions having the Same Denominator.

Worksheet on Subtraction of Fractions having the Same Denominator.

Worksheet on Add and Subtract Fractions.

Worksheet on Fractional Numbers.

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Add Fractions Color by Number: Unlike Denominators & Mixed Numbers

Looking for a different way to practice adding fractions? This simple task card activity is an engaging way to practice. Grab the Add Fractions Color by Number FREE for grades 5-6!

Fraction operations. Whew! Just typing that out feels stressful! Over and over again I hear from teachers whose students struggle with fraction sense and fraction operations . While I do encourage teaching and modeling with hands on tools , pictures and real life contexts , kids also just need lots of practice and exposure . So the next time you’ve got an early finisher, need some low-prep sub plans or want some extra practice to send home, grab this free add fractions color by number activity !

Materials Needed for the Fraction Addition Color by Number:

• Coloring page for each student
• Fraction Addition Task Cards printed & cut (there are 12 altogether)
• Colored pencils, markers or crayons

Once you’ve got the materials printed and prepped and gathered some coloring supplies, you’re all set!

How to Complete the Color by Number Activity:

This low-prep math practice is pretty straightforward. To begin, students solve the fraction and mixed number addition problems on the task cards.

If they find the correct solution, it will be on the task card with the COLOR to use for that task card. They then color the color by number page using the task card number .

For example, the solution for task card #2 is labeled GREEN . In this case, students would color all the 2’s on the color by code page GREEN .

This may be the one thing to note for students before they begin. The FRACTION ANSWERS will not be on the coloring page, only the number of each task card .

Once they have all 12 cards solved, they will be able to color in the design on the coloring page .

One final note about the coloring page : a design was chosen specifically so that students could not just guess the colors and therefore guess the answers . It is a unique design, full of color, rather than a picture of a known object . 😉

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8 !

Learn more about Math Geek Mama+ right HERE .

Ways to Use the Add Fractions Color by Code:

Although you could assign this as an individual activity, you could also put students in small groups or use this as a math center .

In this case, put students in groups of 3-4 . Print a coloring page for each student , but only print and cut out ONE set of task cards .

Then students will each choose 3-4 task cards to solve individually. They can then help each other if they get stuck, and check each other’s work as they go.

Once they have all completed their task cards, they swap to know how to color in the additional spaces on the coloring sheet.

Although this does not provide as much practice for each student, it does allow the activity to be completed faster , requires less printing , and allows students to work collaboratively .

Of course you can also assign this as individual practice or review . Here are some ideas:

• Keep on hand for ready to go sub plans
• Offer as a choice board option
• Activity for early finishers
• For struggling learners who need more practice
• To send home for tutors or parents to practice/review with their kids

However you use this, I hope it provides a new or different option for your kids who need to review addition with fractions and mixed numbers!

Ready to grab the download for yourself? Head to my shop at the link below.

{Click HERE to Go to My Shop & Grab the FREE Add Fractions Color by Number Activity!}

Looking for more fraction resources? Check out these additional freebies:

• {FREE} Candy Bar Fractions: Hands On Fraction Practice
• Add & Subtract Fractions Cut & Paste Activity {FREE}
• Hands On Adding Fractions Game for Kids
• Missing Addend with Fractions: Challenges for Google Slides {FREE}

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Addition of Similar Fractions

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Find the sum of the following fractions.

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