Addition of Unlike Fractions
Step 1: Use LCM method to convert the unlike fractions into like fractions.
Step 2: Find out new numerators of the given fractions.
Step 3: Add new numerators.
Step 4: Write the resulting numerator after addition over the LCM as denominator.
Step 5: If resultant fraction is an improper fraction then convert it into mixed fraction.
Example 1:
Here denominators are different. So, we will first make denominators of the given fractions equal, using LCM method.
LCM OF 3 and 4
= 3 x 4
= 12
Now we have to find out new numerators of the both fractions.
New Numerator of the first fraction =
LCM ÷ Denominator of the first fraction x Numerator of the first fraction
= 12 ÷ 3 = 4 (LCM ÷ Denominator of the first fraction)
= 4 x 1 =4 (Resultant answer x Numerator of the first fraction)
New numerator of first fraction is 4
New Numerator of the second fraction =
LCM ÷ Denominator of the second fraction x Numerator of the second fraction
= 12 ÷ 4 = 3 (LCM ÷ Denominator of the second fraction)
= 3 x 1 =3 (Resultant answer x Numerator of the second fraction)
New numerator of second fraction is 3
Now add new numerators
= 4 + 3
= 7
Then write the resulting numerator after addition over the LCM as denominator.
Example 2:
Here denominators are different. So, we will first make denominators of the given fractions equal, using LCM method.
LCM OF 7, 21 and 14
7 
7, 21, 14 
2 
1, 3 , 2 
3 
1, 3, 1 

1, 1, 1 
= 7 x 2 x 3
= 42
Now we have to find out new numerators of the all the fractions.
New Numerator of the first fraction =
LCM ÷ Denominator of the first fraction x Numerator of the first fraction
= 42 ÷ 7 = 6 (LCM ÷ Denominator of the first fraction)
= 6 x 4 = 24 (Resultant answer x Numerator of the first fraction)
New numerator of first fraction is 24
New Numerator of the second fraction =
LCM ÷ Denominator of the second fraction x Numerator of the second fraction
= 42 ÷ 21 = 2 (LCM ÷ Denominator of the second fraction)
= 2x2 =4 (Resultant answer x Numerator of the second fraction)
New numerator of second fraction is 4
New Numerator of the third fraction =
LCM ÷ Denominator of the third fraction x Numerator of the third fraction
= 42 ÷ 14 = 3 (LCM ÷ Denominator of the third fraction)
= 3x31 =93 (Resultant answer x Numerator of the third fraction)
New numerator of third fraction is 93
Now add all new numerators
= 24 + 4 + 93
= 121
Then write the resulting numerator after addition over the LCM as denominator.
Now convert the improper fraction into mixed fraction
Note:
1. In addition of a whole number and a fractional number, we assume denominator of whole number as 1 for calculation.
2. In addition of mixed fractions, convert mixed fraction into improper fraction before starting to add.