In this worksheet, we will learn how to **simplify** **fractions**.

This process is often carried out at the end of a fraction calculation to make the fraction more simple.

If we divide the top **(the numerator) **and the bottom **(the denominator) **of a fraction by the** same **number we get an **equivalent **fraction.

This is called **simplifying** a fraction.

When we simplify a fraction as much as possible, it is called reducing it to its **lowest terms. **

We do this by dividing the numerator and the denominator by their **highest common factor.**

**Example 1**

Simplify this fraction to its lowest terms

36 |

45 |

**Answer**

We look for the highest number that goes into 36 and 45.

This will be 9, because 4 × 9 = 36 and 5 × 9 = 36.

So we divide the numerator and the denominator by the magic number 9, to get 4 and 5.

36 | = | 4 |

45 | 5 |

We cannot simplify this any further, so the answer is:

4 |

5 |

**Example 2**

Simplify this fraction to its lowest terms.

64 |

96 |

**Answer**

Sometimes it is hard to find the highest common factor.

We look for any number that goes into 64 and 96.

This could be 8, because 8 × 8 = 64 and 12 × 8 = 96.

So we divide the numerator and the denominator by the magic number 8, to get 8 and 12.

64 | = | 8 |

96 | 12 |

Now we can simplify again by looking for the highest number that goes into 8 and 12.

This is 4 because 2 × 4 = 8 and 3 × 4 = 12.

So we divide the numerator and the denominator by the magic number 4, to get 2 and 3.

So the answer is:

2 |

3 |

Let's have a go at the questions now.