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.**