Addition and Subtraction of Fractions

What is Fraction? 

A fraction can be defined as a part of a whole number which can be represented numerically.

For example:

Bheem drank two and a half glass of milk i.e. 2 ½ and Indu drank one and a half glass of milk

i.e. 1 ½ .In this example, the half glass of milk is represented as a numerical quantity.

Introduction to Addition and Subtraction of Fraction

From the above example the question arises, what is the total amount of milk that they drank? In this case, the addition and subtraction of fractions take place to find the total quantity of an item. How do we add fraction? How to subtract fractions? What are the steps to add or subtract?  Let us learn about Addition and Subtraction of Fractions.

Methods for Adding and Subtracting Fractions

Unlike whole numbers adding and subtracting fraction is not easy it requires different methods for different types of fraction. The following methods will guide you through addition and subtraction of fractions.

  • Addition and subtraction of Like fraction

  • Addition and subtraction of unlike fraction

  • Addition and Subtraction of Mixed fraction

Addition and Subtraction of Like Fraction

The fractions which have the same denominators are known as Like fractions.  Additional and subtraction of like fraction is quite easy, as the denominator of the fractions are same.

Example 1:

1/4 + 2/4 =?

In the above example the denominator of the fraction is the same.

                1/4 =      2/4 = 

The above diagram gives the pictorial representation of the fractions. The circle is divided into 4 parts which is the denominator and the colored part represents the numerator.

Steps for Addition of Like Fractions:

Step1: check the denominators of the fraction, If the denominator is the same or not. 

Step2: If the denominators are the same, add the numerators of the fraction keeping the denominator as it is.

Step3: Solution 

         1/4 + 2/4 = 3/4 

Example 2:  6/8 – 2/8 =?

Steps for Subtraction of Like Fractions:

Step1: Check the denominators of the fraction, If the denominator is the same or not.

Step2: Subtract the smaller numerator with the larger one keeping the denominator as it is.

Step3: Solution

 6/8 – 2/8 = 4/8 

Addition and Subtraction of Unlike Fraction

The fractions which have the different denominators are known as unlike fractions. For addition and subtraction of fraction the denominators of the fraction should be the same. So we need to make them the same by taking LCM of the denominators.

Example 34/6 + 2/8 =?

Steps for Addition of Unlike Fractions:

Step 1: Take LCM of the denominators of the given fractions.In this example the LCM of  6 and 8 is 24.

(LCM is the least common multiple of two numbers)

Step 2: To get the same denominator 8 and 12 should be converted into 24 by multiplying the suitable multiple to both numerator and denominator.

For  4/6 ,  4/4  will be multiplied  4/6 x 4/4 = 16/24

For  2/8 ,  3/3  will be multiplied  2/8 x 3/3 = 6/24

Step 3: Now, the denominators of the two fractions are the same .Add the numerator keeping the denominator as it is.

 16/24 + 6/24 

Step 4: Solution

16/24 + 6/24 = 22/24

Example 4:  4/6 - 2/8 =?

Steps for Subtraction of Unlike Fractions:

Step 1: Take LCM of the denominators of the given fractions. In this example the LCM of  6 and 8 is 24.

(LCM is the least common multiple of two numbers)

Step 2: To get the same denominator 8 and 12 should be converted into 24 by multiplying the suitable multiple to both numerator and denominator.

For  4/6 ,  4/4  will be multiplied  4/6 x 4/4 = 16/24

For  2/8 ,  3/3  will be multiplied  2/8 x 3/3 = 6/24

Step 3: Now, the denominators of the two fraction are the same .Subtract the numerator keeping the denominator as it is.

 16/24 - 6/24 

Step 4: Solution

16/24 - 6/24 = 10/24

Addition and Subtraction of Mixed Fraction

A mixed fraction can be defined  as a combination of a whole number and a fraction combined into one mixed number.

For example :  2 1/4   is a mixed fraction

2 1/4    =

In the above diagram the whole number is represented by the circle which is completely colored and the fraction is represented by the circle which is partially colored.

There are two methods for the addition and subtraction of mixed fraction.

  1.  Addition and subtraction of like mixed fraction.

  2.  Addition and subtraction of unlike mixed fraction.

Addition and Subtraction of Like Mixed Fraction

Example 5: 3 3/4 + 2 2/4 =?

Steps for Addition of Like Mixed Fraction 

Step1: First add the whole number of the mixed number

3+2= 5 - (1)

Step 2: Add the fractional part of the mixed number

3/4 2/4 =5/4     -- (2)  

Step 3: Converting improper fraction into proper fraction

Equation (2)  —–> 5/4  = 1 1/4   -- (2) 

Step 4: Solution 

Combining equation (1) and (2)

5+1 1/ =6 1/   

Example 6: 3 3/4 + 2 2/4 =?

Steps for Subtraction of Like Mixed Fraction 

Step1: First subtract the whole number of the mixed number

3-2= 1 - (1)

Step 2: Subtract the fraction part of the mixed number

3/4 2/4 =1/4     -- (2)  

Step 3: Solution 

Combining equation (1) and (2)

1+1/4   =11/4     

Addition and Subtraction of Unlike Mixed Fraction

In Unlike mixed fraction the denominator of the fractional part is different which needs to be made the same using LCM.

Example 7: 3 3/4 + 2 2/6 =?

Steps for Addition of Unlike Mixed Fraction -

Step 1: First add the whole number of the mixed number

3+2= 5 - (1)

Step 2: Take the LCM of the fractional part and make the denominator same

The LCM of 4 and 6 is 12

For  3/4 ,  3/3  will be multiplied  3/4 3/3 = 9/12

For  2/6 ,  2/2  will be multiplied  2/6 x 2/2 = 4/12

Step 3: Adding the fraction with the same denominators 

9/124/12 =13/12     -- (2)  

Step 4: Converting improper fraction into proper fraction

Equation (2) —–> 13/12  =  1 1/12     -- (2)  

Step 5: Solution 

Combining equation (1) and (2)

5+11/12   =61/12   

Example 8: 33/4 – 22/6 =?

Steps for Subtraction of Unlike Mixed Fraction 

Step1: First subtract the whole number of the mixed number

3-2= 1 - (1)

Step 2: Take the LCM of the fractional part and make the denominator same

The LCM of 4 and 6 is 12

For  3/4 ,  3/3  will be multiplied  3/4 3/3 = 9/12

For  2/6 ,  2/2  will be multiplied  2/6 x 2/2 = 4/12

Step 3: Subtracting the fraction with the same denominators 

9/12 4/12 =5/12     -- (2)  

Step 4: Solution 

Combining equation (1) and (2)

5+5/12   =51/12   

FAQ (Frequently Asked Questions)

 Q1. What are the Three Different Types of Fraction?

 Ans. The three different types of fractions are:

  1. Like Fraction

  2. Unlike Fraction

  3. Mixed Fraction

Q2. How do We Add Fractions?

Ans. There are different methods for adding different types of fraction. The common method between them is by making the denominator same to each other and adding the numerator.

Q3. How to Subtract Fractions?

Ans. There are different methods for subtracting  different types of fraction. The common method between them is by making the denominator same to each other and subtracting the greater numerator by the smaller one.