HOW TO FIND SQUARE OF A FRACTION

To obtain the square of a fraction, we have to square both numerator and denominator of the fraction.

For example, let us consider the fraction a/b, where b ≠ 0.

Then, the square of the fraction a/b is 

=  (a / b)²

=  a² / b²

Note :

If two fractions are in addition or subtraction, first we have to add or subtract the fractions and square both numerator and denominator of the resulting fraction.

Example : 

(1/2 + 1/4)²  =  (2/4 + 1/4)²

(1/2 + 1/4)²  =  [(2 + 1) / 4]²

(1/2 + 1/4)²  =  [3 / 4]²

(1/2 + 1/4)²  =  3² / 4²

(1/2 + 1/4)²  =  9 / 16

Example 1 :

Find the square of 7/10.

Solution :

Square of 7/10 is 

=  (7/10)²

=  7² / 10²

=  49/10

Example 2 :

Find the square of [1/12 + 1/3]. 

Solution :

Square of [1/12 + 1/3] is 

=  [1/12 + 1/3]²

=  [1/12 + 4/12]²

=  [(1 + 4)/12]²

=  [5/12]²

=  25/144

Example 3 :

Find the square of [4/15 ⋅ 3/20].

Solution :

Square of [4/15 ⋅ 3/20] is 

=  [4/15 ⋅ 3/20]²

=  [4/15 ⋅ 3/20]²

Simplify.

=  [12/300]²

=  (1 / 25)²

=  1² / 25²

=  1 / 625

Example 4 :

Find the square of (-3/4).

Solution :

Square of (-3/4) is

=  (-3/4)²

=  (-3)² / 4²

  =  9/16

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