ADD AND SUBTRACT FRACTIONS

The following steps would be useful to add or subtract fractions.

Case 1 (fractions with same denominator) : 

When the denominators of the fractions are same, take the denominator once and combine the numerators. Simplify the fraction, if required. 

Case 1 (fractions with different denominator) : 

When the denominators of the fractions are different, find the least common multiple of the denominators and make the least common multiple as denominator for each fraction using multiplication. Now, take the denominator once and combine the numerators. Simplify the fraction if required.  

Example 1 :

Find the value of :

3/4 + 1/4

Solution :

The fractions above have the same denominator, that is 4.

So, take the denominator once and combine the numerators.

3/4 + 1/4 = (3 + 1)/4

= 4/4

= 1

Example 2 :

Find the value of :

7/15 + 13/15 + 11/15

Solution :

The fractions above have the same denominator, that is 15.

So, take the denominator once and simplify the numerators.

7/15 + 13/15 + 11/15 = (7 + 13 + 11)/15

= 31/15

Example 3 :

Find the value of :

10/21 - 3/21

Solution :

The fractions above have the same denominator, that is 21.

So, take the denominator once and simplify the numerators.

10/21 - 3/21 = (10 - 3)/21

= 7/21

= 1/3

Example 4 :

Find the value of :

5/28 + 3/28 - 1/28

Solution :

The fractions above have the same denominator, that is 28.

So, take the denominator once and simplify the numerators.

5/28 + 3/28 - 1/28 = (5 + 3 - 1)/28

= 7/28

= 1/4

Example 5 : 

Find the value of :

1/12 + 3/18

Solution :

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (12, 18) = 36.

Now, make the denominator of each fraction 36 using multiplication.

1/12 = (1 ⋅ 3)/(12 ⋅ 3) = 3/36

3/18 = (3 ⋅ 2)/(18 ⋅ 2) = 6/36

1/12 + 3/18 :

= 3/36 + 6/36

= (3 + 6)/36

= 9/36

= 1/4

Example 6 : 

Find the value of :

5/16 - 7/20

Solution :

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (16, 20) = 80.

Now, make the denominator of each fraction as 80 using multiplication.

5/16 = (5 ⋅ 5)/(16 ⋅ 5) = 25/80

7/20 = (7 ⋅ 4)/(20 ⋅ 4) = 28/80

5/16 - 7/20 :

= 25/80 - 28/80

= (25 - 28)/80

= -3/80

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