ADD AND SUBTRACT FRACTIONS

Add and Subtract Fractions :

In this section, you will learn, how to add and subtract two or more fractions. 

Add and Subtract Fractions - Steps - Key Points

1. When we add or subtract fractions, if the denominators are same, we have to take the denominator once and combine the numerators.

2.  If the denominators are not same, we have to use the method of LCM to add or subtract the fractions. 

3.  If the result is an improper fraction, then convert it into a mixed fraction. 

Add and Subtract Fractions - Examples

Example 1 :

Find the value of :

3/4 + 1/4

Solution :

The given two fractions have the same denominator. That is 4.

So, take the denominator once and simplify the numerators. 

=  (3 + 1) / 4

=  4 / 4

=  1

Therefore, 

3/4 + 1/4  =  1

Example 2 :

Find the value of :

7/15 + 13/15 + 11/15

Solution :

The given fractions have the same denominator. That is 15.

So, take the denominator once and simplify the numerators. 

=  (7 + 13 + 11) / 15

=  31/15

Because 31/15 is an improper fraction, convert it into a mixed number. 

Then, we have 

=  2 1/15

Therefore, 

7/15 + 13/15 + 11/15  =  2 1/15

Example 3 :

Find the value of :

10/21 - 3/21

Solution :

The given fractions have the same denominator. That is 21.

So, take the denominator once and simplify the numerators. 

=  (10 - 3) / 21

=  7 / 21

Simplify. 

=  1 / 3

Therefore, 

10/21 - 3/21  =  1/3

Example 4 :

Find the value of :

5/28 + 3/28 - 1/28

Solution :

The given fractions have the same denominator. That is 28.

So, take the denominator once and simplify the numerators. 

=  (5 + 3 - 1) / 28

=  7 / 28

Simplify. 

=  1 / 4

Therefore, 

5/28 + 3/28 - 1/28  =  1/4

Example 5 : 

Find the value of :

1/12  +  3/18

Solution :

The given two fractions are unlike fractions. Because, they have different denominators. 

Because the denominators are not same, we have to use the method of LCM to add the above fractions. 

LCM of (12 and 18)  =  36

Now, make the denominators of both the fractions to be 36.

To make the denominator to be 36, we have to multiply the numerator and denominator of the first fraction by 3 and the second one by 2.

Then, we have  

1/12  +  3/18  =  3/36  +  2/36

1/12 + 3/18  =  (3 + 2) / 36

1/12 + 3/18  =  5 / 36

Example 6 : 

Find the value of :

5/16 - 7/20

Solution :

The given two fractions are unlike fractions. Because, they have different denominators. 

Because the denominators are not same, we have to use the method of LCM to add the above fractions. 

LCM of (16 and 20)  =  80

Now, make the denominators of both the fractions to be 80.

To make the denominator to be 80, we have to multiply the numerator and denominator of the first fraction by 5 and the second one by 4.

Then, we have  

5/16 - 7/20  =  25/80 - 28/80

5/16 - 7/20  =  (25 - 28) / 80

5/16 - 7/20  =  3/80

After having gone through the stuff given above, we hope that the students would have understood, how to add two or more fractions. 

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