# Square of Fractions

In this chapter you will learn to find square of fraction number with examples.

Review the concept of fractions by clicking the red link.

If you want to learn about the squares of number, click the link.

## Representing square of fraction

While squaring number, we multiply the number by itself twice.

If \mathtt{\frac{a}{b}} is a fraction, then the square of the fraction is represented as \mathtt{\left(\frac{a}{b}\right)^{2}}

## How to calculate the square of fraction ?

If \mathtt{\frac{a}{b}} is the given fraction, then it square can be calculated by following below steps;

(a) Multiply the fraction by itself

(b) Multiply the numerator and denominator separately

(c) If possible, simplify the resulting fraction

The above process can be generalized as follows;

\mathtt{\left(\frac{a}{b}\right)^{2} \Longrightarrow \frac{a\times a}{b\times b} \ \Longrightarrow \frac{a^{2}}{b^{2}}}

I hope you understood the above process. Let us solve some examples related to square of fractions.

## Example of Square of Fraction

Example 01
Find the square of fraction 3 / 5

Solution
\mathtt{\Longrightarrow \left(\frac{3}{5}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3\times 3}{5\times 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{9}{25}}

Hence, 9 / 25 is the square of given fraction.

Example 02
Find the square of fraction 11 / 15

Solution
\mathtt{\Longrightarrow \left(\frac{11}{15}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{11\times 11}{15\times 15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{121}{225}}

Hence, 121 / 225 is the square of given fraction.

Example 03
Find the square of fraction 1 / 9

Solution
\mathtt{\Longrightarrow \left(\frac{1}{9}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1\times 1}{9\times 9}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{81}}

Hence, 1 / 81 is the square of fraction 1 / 9

Example 04
Find the square of fraction \mathtt{\frac{-4}{13}}

Solution
To understand the concept of
square of negative number, click the red link.

Squaring the above fraction;

\mathtt{\Longrightarrow \left(\frac{-4}{13}\right)^{2}}\\\ \ \mathtt{\Longrightarrow \ \frac{-4\times -4}{13\times 13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{169}}

Hence, 16 / 169 is the square of given fraction.

Example 05
Find the square of fraction \mathtt{\frac{-3}{10}}

Solution

\mathtt{\Longrightarrow \left(\frac{-3}{10}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3\times -3}{10\times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{9}{100}}

Hence, 9 / 100 is the square of fraction -3 / 10

Example 06
Find the square of fraction 10 / 14

Solution
The fraction can be simplified further.

Divide numerator & denominator by 2

\mathtt{\Longrightarrow \ \frac{10\div 2}{14\div 2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{10} \ 5}{\cancel{14} \ 7\ }}\\\ \\ \mathtt{\Longrightarrow \frac{5}{7}}

The fraction has been reduced to 5 / 7

Now squaring the fraction, we get;

\mathtt{\Longrightarrow \left(\frac{5}{7}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5\times 5}{7\times 7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{25}{49}}

Hence, 25 / 49 is the square of given fraction.

Example 07
Find the square of fraction 6 / 33

Solution
The fraction can be simplified further.

Divide numerator and denominator by 3.

\mathtt{\Longrightarrow \ \frac{6\div 3}{33\div 3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{6} \ 2}{\cancel{33} \ 11\ }}\\\ \\ \mathtt{\Longrightarrow \frac{2}{11}}

The fraction has been simplified to 2 / 11.

Squaring the fraction 2 / 11, we get;

\mathtt{\Longrightarrow \left(\frac{2}{11}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2\times 2}{11\times 11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{121}}

Hence, 4 / 121 is the solution of given fraction.

Example 08
Find the square of fraction -7 / 63

Solution
The fraction can be simplified further.

Divide numerator and denominator by 7.

\mathtt{\Longrightarrow \ \frac{-7\div 7}{63\div 7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{-7} \ -1}{\cancel{63} \ 9}}\\\ \\ \mathtt{\Longrightarrow \frac{-1}{9}}

Hence, the fraction has been simplified to – 1 / 9

Squaring the above fraction.

\mathtt{\Longrightarrow \left(\frac{-1}{9}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-1\times -1}{9\times 9}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{81}}

Hence, 1 / 81 is the solution of given fraction.