# HOW TO FIND THE SQUARE OF A FRACTION

## About "How to find the square of a fraction"

How to find the square of a fraction ?

Here we are going to see how to find the square of fraction.

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

For example,

(a / b)2  =  a2 / b2

We should not take squares for the terms which are added or subtracted.

After converting two or more rational numbers as one rational number, we may take squares for both numerator and denominator separately.

Fro example,

[ (1/2) + (1/4) ]2  =  ( (2 + 1)/4 )2

=  (3/4)2

=  32 / 42

=  9 / 16

Let us look into some more examples based on the concept given above.

Example 1 :

Find the square of 7/10

Solution :

Square of 7/10  =  (7/10)2

=  72 / 102

=  (7 ⋅ 7)  / (10 ⋅ 10)

=  49/10

Example 2 :

Find the square of (1/12) + (1/3)

Solution :

Square of (1/12) + (1/3)  =  [(1/12) + (1/3)]2

Since we have square for two rational number which are added, we have to convert it into one rational number by taking L.C.M.

=  [(1/12) + (1/3) ⋅ (4/4)]

=  [(1/12) + (4/12)]

=  (1 + 4) / 12

=  5/12

[(1/12) + (1/3)]2  =  (5/12)2

=  52 / 122

=  25/144

Example 3 :

Find the square of (4/15)  (3/20)

Solution :

Square of (4/15)  (3/20)  =  [(4/15)  (3/20)]2

Since we have square for two rational number which are multiplied, we may simplify the rational numbers and take squares.

=  [(4/15)  (3/20)]2

=  [(4 ⋅ 3) / (15 ⋅ 20)]2

=  [ (1 ⋅ 1) / (5 ⋅ 4) ]2

=  (1 / 20)2

=  12 / 202

=  1 / 400

Example 4 :

Find the square of (-3/4)

Solution :

Square of negative is positive.

square of (-3/4)  =  (-3/4)2

=  (-3)2 / 42

=  9/16

To find the square of the algebraic expression, we have to compare the given algebraic expression with one of the following algebraic identities given below and expand.

(a + b)2  =  a2 + 2ab + b2

(a - b)2  =  a2 - 2ab + b2

(a + b + c)2  =  a2 +  b2 + c2 + 2ab + 2bc + 2ca

To see more example please visit "Algebraic identities" After having gone through the stuff given above, we hope that the students would have understood "How to find the square of a fraction"

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