# Equivalent Fractions

## What are Equivalent Fractions?

Equivalent fractions are any two fractions that, as you would expect, are equivalent (or equal). If your child, or children, are really struggling with the concept of equivalent fractions then start by allowing them to understand, first of all, that one half is the same as two quarters. One half and two quarters are equivalent fractions, $\frac{1}{2}=\frac{2}{4}$. In the picture on the left, you can see that one whole is the same as two halves, one whole is also the same as four quarters and one whole is the same as six sixths. These are all equivalent fractions that so happen to be equal to a whole.

## How to know when fractions are equivalent

If you multiply the top and bottom of a fraction by the same number, the result will be an equivalent fraction. Don’t forget that the top of a fraction is the numerator and the bottom of a fraction is the denominator and so, in other words, multiplying the numerator and denominator of a fraction by the same number results in an equivalent fraction. For example, take the fraction $\frac{2}{5}$ and multiply the top and bottom by 3:

$\frac{2}{5}$ and $\frac{6}{15}$ are equivalent fractions.

## Simplifying Fractions

The same applies for division. If you divide the top and bottom of a fraction by the same number  the result will be an equivalent fraction. For example, take the fraction  $\frac{10}{25}$ and divide top and bottom by 5:  $\frac{10}{25}$ and $\frac{2}{5}$ are equivalent fractions. This process is known as simplifying fractions.

Now consider the fraction $\frac{14}{42}$. By dividing the top and bottom by 2 we get $\frac{7}{21}$. This is an equivalent fraction but it is not the simplest one. By dividing the top and bottom of this fraction by 7 we get $\frac{1}{3}$. This is the simplest equivalent fraction. Simplifying a fraction is not complete until it is as simple as it gets. Quite often children think that they cannot simplify the fraction if it cannot be divided, top and bottom, by 2. Encourage them to remember that they can divide the top and bottom of fractions by other numbers and they should go through those numbers until they are sure.