# Simplifying Fractions

#### Back to Foundation Maths

## Description

This is an introductory tutorial outlining what simplified fractions are, why we simplify them, and how to simplify them. The associated video tutorial is to come.

## What does it mean to simplify a Fraction?

*Simplifying* a fraction means to make it simpler.

## Why Simplify a Fraction?

We simplify fractions to make them *easier to understand* and *easier to work with*.

#### An example

**You have a cake that weighs 400g. When a friend comes to visit, you send them home with 150g of the cake to share with their partner. What fraction of the cake have you given them?**

We know that the numerator will be the amount of cake you gave to your friend (150g) and the denominator will be how much the whole cake weighed. Therefore, the answer is: the fraction of the cake you've given them is ^{150}/_{400}. This is correct, however let's see if we can make it simpler.

## How to Simplify a Fractions

To simplify a fraction, you need to follow three simple steps.

### Step 1: Write down each number's factors

The *factors* of a number are all of the numbers that can divide evenly into that number.

### Step 2: Identify the largest common factor

NB: Another term for *largest common factor* is

*largest common*. This is because when you

**denominator***divide a number*by a factor, that factor becomes the denominator.

### Step 3: Divide both numbers by largest common factor

So, you can say that you gave your friend ^{150}/_{400} OR ^{3}/_{8} of the cake. The fraction ^{3}/_{8} is much simpler to understand - you gave them three slices of a cake that was cut into eight slices. Now that you can see how it works, why don't you have a go at a few exercises below.

## Complementary Exercises

Below are some complementary exercises for you to work through in your own time to consolidate your understanding of how to simplify fractions (answers are included!). You can download the document here: