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Subtraction of Fractions with Like Denominators

Subtraction of fractions with like denominators requires you to subtracting the numbers in the numerator of the respective fractions, and writing the common denominator for the denominator. For example:

a.  2/3 – 1/3  = {2~-~1}/3  =  1/3

b.  4/7 – 2/7  = {4~-~2}/7  =  2/7

When we subtract two mixed numerals with common denominator, we subtract the whole numbers separately and add the subtraction of the fractions. For example:

a.  24/5 – 12/5

=  (2 – 1) + (4/52/5)

= 1 + 2/5  =  12/5

b.  216/17 – 14/17

=  (2 – 1) + (16/174/17)

= 1 + 12/17  =  112/17

c.  216/17 – 1

=  (2 – 1) + 16/17

= 1 + 16/17  =  116/17

 

When we have to subtract two fractions or mixed numerals where the second fraction is larger than the first one, we obey the following steps:

  • subtract 1 from the whole number and add to the adjacent fraction of there is one
  • subtract the whole numbers and fractions and put together
  • simplify where possible

For example:

a.  4 – 15/12

=  312/12 – 15/12

= (3 – 1) + ({12/12}~-~{5/12})

= 2 + 7/12   =  27/12

b.  62/5 –  34/5    (2/5 is smaller than 4/5), so..

(55/52/5)  –  34/5

= 57/5  –  34/5

= (5 – 3) + (7/5 – 4/5)

= 2 + 3/5   =  23/5

c.  43/10 –  29/10

(310/103/10)  –  29/10

= 313/10  –  29/10

= (3 – 2) + (13/10 – 9/10)

= 1 + 4/10   =  12/5

 

We now look at subtraction of fractions with different denominators