addition and subtraction of fraction problem solving

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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Fractions  - Adding and Subtracting Fractions

Fractions  -, adding and subtracting fractions, fractions adding and subtracting fractions.

Fractions: Adding and Subtracting Fractions

Lesson 3: adding and subtracting fractions.

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Adding and subtracting fractions

In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.

In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.

Click through the slideshow to learn how to set up addition and subtraction problems with fractions.

Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.

You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.

When you add fractions, you just add the top numbers, or numerators .

That's because the bottom numbers, or denominators , show how many parts would make a whole.

We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.

So we only need to add the numerators of our fractions.

We can stack the fractions so the numerators are lined up. This will make it easier to add them.

And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.

We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.

If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.

Just like when we added, we'll stack our fractions to keep the numerators lined up.

This is because we want to subtract 1 part from 3 parts.

Now that our example is set up, we're ready to subtract!

Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!

You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.

You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.

Your gas tank is 2/5 full, and you put in another 2/5 of a tank.

Solving addition problems with fractions

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.

Click through the slideshow to learn how to add fractions.

Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Remember, when we add fractions, we don't add the denominators.

This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .

3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.

The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.

3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.

Let's try another example: 7/10 plus 2/10 .

Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .

7 plus 2 equals 9 , so we'll write that to the right of the numerators.

Just like in our earlier example, the denominator stays the same.

So 7/10 plus 2/10 equals 9/10 .

Try solving some of the addition problems below.

Solving subtraction problems with fractions

Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!

Click through the slideshow to learn how to subtract fractions.

Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.

Just like in addition, we're not going to change the denominators.

We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.

We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.

Just like when we added, the denominator of our answer will be the same as the other denominators.

So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.

Let's try solving another problem: 5/6 minus 3/6 .

We'll start by subtracting the numerators.

5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.

As usual, the denominator stays the same.

So 5/6 minus 3/6 equals 2/6 .

Try solving some of the subtraction problems below.

After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .

Adding fractions with different denominators

On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.

In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .

We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.

Click through the slideshow to learn how to add fractions with different denominators.

Let's add 1/4 and 1/3 .

Before we can add these fractions, we'll need to change them so they have the same denominator .

To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .

It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .

Since 12 is the LCD, it will be the new denominator for our fractions.

Now we'll change the numerators of the fractions, just like we changed the denominators.

First, let's look at the fraction on the left: 1/4 .

To change 4 into 12 , we multiplied it by 3 .

Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .

1 times 3 equals 3 .

1/4 is equal to 3/12 .

Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.

Our old denominator was 3 . We multiplied it by 4 to get 12.

We'll also multiply the numerator by 4 . 1 times 4 equals 4 .

So 1/3 is equal to 4/12 .

Now that our fractions have the same denominator, we can add them like we normally do.

3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .

Try solving the addition problems below.

Subtracting fractions with different denominators

We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.

Click through the slideshow to learn how to subtract fractions with different denominators.

Let's try subtracting 1/3 from 3/5 .

First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .

It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.

Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .

5 times 3 equals 15 . So our fraction is now 9/15 .

Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .

Now that our fractions have the same denominator, we can subtract like we normally do.

9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .

Try solving the subtraction problems below.

Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.

5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.

Let's add these two mixed numbers: 2 3/5 and 1 3/5 .

We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .

As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .

2 times 5 equals 10 .

Now, let's add 10 to the numerator, 3 .

10 + 3 equals 13 .

Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .

Now we'll need to convert our second mixed number: 1 3/5 .

First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .

Next, we'll add 5 to the numerators. 5 + 3 = 8 .

Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .

Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .

Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .

The answer, 4, will become our whole number.

And the remainder , 1, will become the numerator of the fraction.

So 2 3/5 + 1 3/5 = 4 1/5 .

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Add & Subtract Fractions for Grade 5

Add & subtract like and unlike fractions.

These grade 5 worksheets provide practice in adding and subtracting fractions with both like and unlike denominators .

Sample Grade 5 Adding Fractions Worksheet

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Key to Fractions Workbooks

These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end.

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Add and Subtract Fractions Online practice for grades 3-7

On this page, you can practice addition and subtraction of fractions. Each practice set will automatically include both addition and subtraction problems.

The options are:

• You can limit the fractions in the problems to like fractions (fractions with the same denominator), for example: 1/6 + 4/6.
• You can limit the script to use only proper fractions—fractions that are less than 1. With this option, the script will make problems such as 1/4 + 2/5, but will not make problems such as 8/5 − 4/5.
• When you choose problems that use simplified fractions, the script will only include fractions in the problems that are in lowest terms. For example, you could get a problem such as 5/6 + 3/5, but you would not see 2/4 + 6/8.
• The last option, when chose, allows or accepts answers to not be in lowest terms. In other words, the script will accept an answer such as 8/10.

Note: ALL answers have to be given as mixed numbers, when possible. In other words, your answer cannot be left as an improper fraction.

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Subtracting fractions word problems

Subtracting fractions word problems: 4 real-life examples.

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Adding fractions word problems

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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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Addition and Subtraction Fraction Word Problems Worksheets

Math word problems are sentence-based exercises that more often, than not, describe real world scenarios and situations that you may run into on your daily routine. Students should have some basic experience with these types of problems. The particular type of problems that we explore on this page focus on those that include a fractional value. To help acclimate students to using factions in this form, we focus solely on the use of addition and/or subtraction operations. Students will first identify the needed math operation(s) and then on the math involved when working with fractions. These worksheets help students identify the operations that should take place between fraction in a word problem.

Aligned Standard: Grade 4 Fractions - 4.NF.3

• Subtraction of Fractions Step-by-Step Lesson - Jack is just giving his popcorn away.
• Guided Lesson - Jello, walking to the market, and spinach soup. All calculations I make everyday, less the spinach.
• Guided Lesson Explanation - This set of instructions is clear and concise with minimal distractions.
• Fraction Word Problems 5-Pack - Five pages of repeated problems to help hammer home the concepts of this area.
• Fraction Word Problems (Word-Based Numbers) 5-Pack - There are no numbers in the questions. The numbers are written as words.
• Practice Worksheet - 2 pages with 10 problems that are full out. There is space to work, too.
• Matching Worksheet - Sorry, but the units kind of give this one away.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

I tried to tie the fractions to things that we use fraction unit with every day (distance, recipes, food, etc.)

• Homework 1 - During the movie Max drinks 5/7 of a cup of water and Luke drinks 1/7 a cup of water. How much more did Max drink?
• Homework 2 - There are 24 hours in a day. Edward has spent 3/8 of the day in school. How much time will Edward spend in school?
• Homework 3 - Laura baked 2 cakes in a microwave. Cake one takes 8/12 of an hour to bake. Cake number two takes 5/12 of an hour to bake. How much more time did cake one take?

Practice Worksheets

These problems are a bit more wordy, if you will. The go is to increase their reading stamina within word problems.

• Practice 1 - Alexis had 5/8 of a pound of sugar yesterday, but today he had 3/8 of a pound of sugar left. How much sugar did Alexis use?
• Practice 2 - Grace is making rice for her family. The boys eat 4/7 of a bag of rice and the girls eat 3/7 of a bag of rice. How much more rice did boys eat than the girls?
• Practice 3 - There are 12 months in a year. Luke has to go on vacation for 1/6 of the year. How much time will Luke spend on holiday?

Math Skill Quizzes

These get us heading to be ready for unit rates. We also have a few applied unit rate questions in here too.

• Quiz 1 - Alana used 5 kg of sugar in 15 days. How much sugar did she use in 120 days?
• Quiz 2 - Dylan bought 6/11 of a kg of apples and 4/11 of a kg of peaches. How much more did the apples weigh than the peaches?
• Quiz 3 - Lincoln has 35 candies and Callus has 28 candies. What fraction of the candies does Lincoln have?

How Do You Identify That A Word Problem Calls for Addition or Subtraction?

There are a series of words and phrases that can be found in most word problems that will indicate to you the math operations involved. The common phrases that indicate finding a sum or the addition operations include, but are not limited to: add to, all together, increased by, more than, and go up by. The words that are commonly found in addition-based word problems include: both, combine, perimeter, plus, sum, and total. The phrases that are often used to indicate that you need to subtract are: decreased by, fewer than, how many more, less than, and take away. The words that are common to subtracting are: difference, left, less, minus, and remaining. Not all the problems will contain these terms, but you can be sure many of them will.

How Do You Solve Problems Like This?

Once you can determine the operations that will be required for you to solve these types of problem, you will run into situations where the math gets in the way. This happens quite often when you run into mixed numbers in these types of word problems. You must have seen mixed numbers quite a few times in your math book. Before you get into adding or subtracting mixed numbers, first make sure you realize what they are. In fractions, mixed numbers are those that have an integer and a proper fraction. Much as they look intimidating, adding and subtracting mixed numbers that have the same denominators is not difficult, in fact it's pretty easy. Let's learn step by step addition and subtraction of mixed numbers with like denominators.

The first step is to convert both the mixed numbers into improper fraction. In case you want to know what, an improper fraction is; it is a fraction having greater numerator and smaller denominator. The way to covert mixed number into an improper fraction to multiplying the denominator with the integer and then adding the numerator into the answer.

2 3/4 - Multiply 4 (denominator) with 2 (integer) and add 3 (numerator) in the result. The result is 11/4.

After you have two improper fractions, add the numerators of the equation. Make sure that the denominators are same, else numerators can't be added. If the result is an improper fraction, reduce it into a mixed number.

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Adding and Subtracting Fraction Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

16 June 2015

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Helpful sheet for practicing wordy fraction questions. Answers can sometimes be simplified further.

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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

Mixed Numbers Calculator

Simplify fractions calculator, decimal to fraction calculator, fraction to decimal calculator, big number fraction calculator.

Use this calculator if the numerators or denominators are very big integers.

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Simplification:

Converting between fractions and decimals:, common engineering fraction to decimal conversions.

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

Story Problems: Addition and Subtraction

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Course: Class 8   >   Unit 8

• Adding polynomials
• Adding algebraic expressions
• Subtracting polynomials

Subtracting algebraic expression

• (Choice A)   9 b 3 − 10 b 2 − 16 b ‍   A 9 b 3 − 10 b 2 − 16 b ‍  
• (Choice B)   9 b 3 ‍   B 9 b 3 ‍  
• (Choice C)   4 b 3 − 3 b 2 ‍   C 4 b 3 − 3 b 2 ‍  
• (Choice D)   4 b 3 − 16 b ‍   D 4 b 3 − 16 b ‍