## Topic outline

• ### 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 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

= 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

= 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.

• 