# Equivalent Fractions and Simplest Form

## What Are Equivalent Fractions?

Equivalent fractions are fractions that show the same part of the whole, even though they look different.

## Examples of Equivalent Fractions

The following fractions are all equivalent to ^{1}/_{2} (one half):

They represent the same part of the whole, but have a different top number (called the numerator) and a different bottom number (called the denominator).

## How to Find Equivalent Fractions

You can make equivalent fractions by multiplying or dividing the numerator and denominator by the same number.

The bottom number of our fraction (called the denominator) is 4. It tells us to divide the cake into 4 equal parts.

In our example above, equivalent fractions of ½ are found by multiplying **both** the numerator and denominator by 2.

## Simplifying (or Reducing) Fractions

Just as equivalent fractions can be found by multiplying both top and bottom by the same number, equivalent fractions can also be found by dividing top and bottom by the same number.

This is called **cancelling**. It simplifies (or reduces) fractions.

In our example above, equivalent fractions are found by dividing **both** the numerator and denominator by 2.

## Simplest Form

A fraction is in its simplest form if the top and bottom numbers cannot be made any smaller by cancelling (while still being whole numbers).

The simplest form of a fraction is the equivalent fraction with the smallest possible numbers.