Equivalent fractions refer to fractions that look different but have the same value. When two or more fractions have the same value but look different are called equivalent fractions. Let’s look at this example below

\text{Example}\space\frac{2}{3} = \frac{4}{6}\\ \text{In this example\space} \frac{4}{6} \text {\space is an equivalent fraction of \space } \frac{2}{3}

But how can you do this? This is simply done by following the Steps below. Let’s look at how to find equivalent fractions of a given fraction.

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## How to find equivalent fractions

To find the equivalent fractions of a given fraction, there are two main ways.

• Multiplying

• Dividing (Cancellation)

**Steps in finding Equivalent fractions using multiplication**

In this method, Equivalent fractions are formed by Multiplying the numerator (top) number and the denominator (bottom) number by the same number. Let’s look at an example

\text{Example 1: find the three Equivalent fraction of \space} \frac{3}{4}\\ \space Ans: \text{To do this Multiply the top number and the down number by 2}\\\space \space \frac{2×3}{2×4}= \frac{6}{8}\\\text{\space} \\

\text{Multiply}\space \frac{3}{4} \space\text{again by } 3=\space\frac{3×3}{3×4}=\frac{9}{12}\\

\text{Then multiply} \space \frac{3}{4} \space\text{by}\space4=\frac{4×3}{4×4}=\frac{12}{16}

\text{Hence, the equivalent fraction of } \space \frac{3}{4}=\frac{6}{8}=\frac{9}{12}.

Therefore, to find the equivalent fraction of a given fraction, multiply the numerator (top) number and the denominators (bottom) by 2,3,4,5… In turns.

This method is pretty cool, right?

Let’s look at the second method

## Finding equivalent fractions Using the cancellation method

To find an equivalent fraction using the cancellation method, divide the top and the bottom number by the same number and this will also give you the equivalent fraction of a given number.

\text{Example1; find the equivalent fraction of }\frac{18}{30}\\ \text{ Answer: divide the top and bottom of the Fraction by}\space2\space=\frac{18\div2}{30\div2}=\frac{9}{15}

\text{Divide}\space\frac{9}{15}\space\text{by}\space3 = \frac{9÷3}{15÷3}=\frac{3}{5}\\ \text{Hence, the Equivalent of fractions of }\space\frac{18}{30}=\frac{9}{15}=\frac{3}{5}