# Equivalent Fractions

## What are equivalent fractions?

Any two fractions with same numerical value is known as equivalent fractions.

For example, \mathtt{\frac{1}{2}} and \mathtt{\frac{2}{4}} are equivalent fractions because value of both the fractions are same.

How can \mathtt{\frac{1}{2}} and \mathtt{\frac{2}{4}} be similar in value?

If you simplify the fraction \mathtt{\frac{2}{4}} you will get fraction \mathtt{\frac{1}{2}} .

\mathtt{\frac{2}{4} \ can\ be\ written\ as;}\\\ \\ \mathtt{\Longrightarrow \ \frac{1\ \times \ 2}{2\ \times 2}}\\ \\
Removing 2 from Numerator & Denominator, we get:

\mathtt{\Longrightarrow \ \ \frac{\ 1\ }{2}}

Hence, on simplification we found that value of \mathtt{\frac{2}{4}} is same as \mathtt{\frac{1}{2}} , so they are equivalent fraction.

\mathtt{\frac{\ 1\ }{2} \ =\ \frac{2}{4}}

### Showing Equivalent Fractions in Graphical Form

We know that fraction \mathtt{\frac{1}{2}} represents half part of any object.

Given below is the image of half shaded rectangle.

Here \mathtt{\frac{1}{2}} means that the figure is divided into two parts and one part of it is shaded.

Similarly, fraction \mathtt{\frac{2}{4}} tells that the same figure is divided into 4 parts out of which 2 part is shaded.

If you compare both the figures you will find that in both the image half of the rectangle is shaded. It means that, \mathtt{\frac{\ 1\ }{2} \ =\ \frac{2}{4}}

## How to make equivalent fractions?

You can make equivalent fractions using two methods:

(A) Multiplication of numerator and denominator with same number
(B) Division of numerator and denominator with same number

We will learn both the methods in this post.

### Multiplication Method for forming Equivalent Fraction

In any fraction, if you multiply numerator and denominator with the same number you will get equivalent fraction.

Let us understand the process with examples.

Example 01
Let we take fraction \mathtt{\frac{3}{4}}

Multiply numerator & denominator by 2

\mathtt{\Longrightarrow \ \frac{3\ \times \ 2}{4\ \times 2} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{6}{8} \ }

The fraction \mathtt{\frac{3}{4}} and \mathtt{\frac{6}{8}} are equivalent fractions.

Similarly, multiply numerator & denominator by 3

\mathtt{\Longrightarrow \ \frac{3\ \times \ 3}{4\ \times 3} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{9}{12} \ }

Again, fraction \mathtt{\frac{3}{4}} , \mathtt{\frac{6}{8}} and \mathtt{\frac{9}{12}} are equivalent since their basic value is same.

Example 02

Consider fraction \mathtt{\frac{5}{7}} for this example.

Multiplying numerator and denominator by 2

\mathtt{\frac{5}{7} \Longrightarrow \ \frac{5\ \times \ 2}{7\ \times 2} \ \Longrightarrow \frac{10}{14} \ } \\\ \\

Now multiply numerator and denominator by 3

\mathtt{\frac{5}{7} \Longrightarrow \ \frac{5\ \times \ 3}{7\ \times 3} \ \Longrightarrow \frac{15}{21} \ }

Here the fractions, \mathtt{\ \frac{5}{7} ,\ \frac{10}{14\ } \ \&\ \frac{15}{21} \ } are equivalent fractions.

### Division Method for forming equivalent fraction

In any fraction, if you divide the numerator and denominator with same number you will get equivalent fraction.

Example:
Let us consider the fraction \mathtt{\frac{12}{8}}

Divide numerator and denominator by 2

\mathtt{\frac{12}{8} \Longrightarrow \ \frac{12\ \div \ 2}{8\ \div \ 2} \ \Longrightarrow \frac{6}{4}}

Here both the fractions \mathtt{\frac{12}{8} \ and\ \ \frac{6}{4} \ } are equivalent fraction.

Note: You have to divide numerator and denominator with the same number otherwise the fraction will not be equivalent.