**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.