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 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.

       

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