Addition and Subtraction of Unlike Fractions.

ADDING AND SUBTRACTION OF UNLIKE FRACTIONS:

Steps to find Addition or Subtraction of Unlike fractions:

a. We need to convert Unlike fractions into Equivalent fractions with common denominators. i.e; Like fractions.

 (i) Need to find L.C.M of denominators.

 (ii) Converting Unlike fractions into Equivalent fractions.

 (iii) Thus, formed Like fractions are Required fractions.

b. Addition or Subtraction of Fractions = We need to add or subtract the Numerators, which gives the required solution.

 

ADDITION OF UNLIKE FRACTIONS:

1)  3/8 + 1/6

Solution:

Given fractions: 3/8 , 1/6 ; Unlike Fractions. Denominators = 8, 6.

a. Converting Unlike fractions into Like fractions:

   (i) L.C.M of denominators = L.C.M ( 8,6 ) = 24.

   (ii) Equivalent fractions: 3/8 = 9/24 ;  1/6 = 4/24.

   (iii) Thus, Required fractions = 9/24 , 4/24 ; Like fractions. 

b. Addition of given fractions = Addition of Equivalent fractions.

   = 3/8 + 1/6  

   =  9/24 + 4/24  

   =  13/24.

 

2) 3/7 + 2/3 + 1/3

Solution:

Given fractions: 3/7, 2/3, 1/3; Unlike fractions. Denominators = 7 , 3, 3.

a. Converting Unlike fractions into Like fractions:

    (i) L.C.M of denominators = L.C.M ( 7 , 3, 3 ) = 21.

    (ii) Equivalent fractions: 3/7 = 9/21 ;  2/3 = 14/21 ;  1/3 = 7/21.

    (iii) Thus, Required fractions = 9/21, 14/21, 7/21 ; Like fractions.

b. Addition of given fractions =  3/7 + 2/3 + 1/3

    = 9/21 + 14/21 + 7/21

    = 30/21.

3)  3/5 – 2/9

Solution:

Given fractions = 3/5 , 2/9 ; Unlike fractions. Denominators = 5, 9.

a. Converting Unlike fractions into Like fractions.

   (i) L.C.M of denominators = L.C.M ( 5,9 ) = 45.

   (ii) Equivalent fractions: 3/5 = 21/45 ; 2/9 = 10/45.

   (iii) Thus, Required fractions = 21/45 , 10/45 ; Like fractions.

b. Subtracting  given fractions = 3/5 – 2/9

    = 21/45 – 10/45

    = 11/45.

     

4) 5 + 6/7

Solution:

Given fractions: 5/1 , 6/7; Unlike fractions. Denominators = 1, 7.

a. Converting Unlike fractions into Like fractions.

    (i) L.C.M of denominators = L.C.M ( 1 , 7 ) = 7.

    (ii) Equivalent fractions:  5/1 = 35/1 ;  6/7 = 6/7.

    (iii) Thus, required fractions = 35/1 , 6/7 ; Like fractions.

b. Addition of given fractions = 5 + 6/7

    = 35/1 + 6/7

    = 41/7.  

 

5) 3 – 1/5

Solution:

Given fractions: 3/1 , 1/5 ; Unlike fractions. Denominators = 1 , 5.

a. Converting Unlike fractions into Like fractions.

    (i) L.C.M of denominators = L.C.M ( 1 , 5 ) = 5.

    (ii) Equivalent fractions:  3/1 = 15/1 ;  1/5 = 1/5.

    (iii) Thus, required fractions = 15/1 , 1/5 ; Like fractions.

b. Subtracting given fractions = 3 – 1/5

    = 15/1 – 1/5

    = 14/5.