Myriora Maths › Maths foundations › Chapter 9: Fractions

Simplifying fractions

Ages 7–9Chapter 9 · Lesson 4

In this lesson

Simplifying makes bigger pieces, but keeps the same amount.
Divide the top and the bottom by the same number.
And the highest common factor does it in one step.

Your turn

Simplify twenty-four thirty-sixths.

Show the answer

The highest common factor is twelve. Twenty-four divided by twelve is two, and thirty-six divided by twelve is three. Two thirds! Four sixths is the same amount, but it isn't the simplest.

The common mistake

Here's a question that catches lots of people. How do you simplify twelve eighteenths? Some people take six from the top and the bottom, and get six twelfths. But that's only one half! It's not the same amount as two thirds. Always divide. Never subtract.

Try it at home

Cut a pizza or a chocolate bar: are 4 of 8 pieces the same as a half? Simplify the fractions you spot.

Practise it as a puzzle. In Factor Gems, every gem is a number, and four gems that share a prime factor divide each other down. Spotting factors becomes the way to play.

Play Factor Gems free in your browser

The one-minute version

Read the whole lesson

Hello, and welcome to Myriora Maths! Here's a fraction: twelve eighteenths. Can we make it simpler? Today, we'll see what simplifying really means.

Why simplify? Imagine a pizza cut into eighteen slices, and you eat twelve of them. Saying you ate twelve eighteenths is a mouthful. Saying you ate two thirds of the pizza is much easier to picture. It's the same with test scores: twelve out of eighteen is just as good as two out of three.

A fraction is a number of equal pieces. Here's a bar cut into eighteen pieces, and twelve of them are shaded. Now let's group the pieces in sixes. Twelve small pieces become two big pieces. Eighteen become three. Same amount of bar. Just bigger pieces. Two thirds!

Method one: divide the top and the bottom by the same number, again and again. Twelve and eighteen are both even, so divide by two. Six ninths. Both divide by three. Two thirds. Two and three share no factors, so we're done.

Method two is quicker. Find the highest common factor: the biggest number that divides both. For twelve and eighteen, it's six. Divide by six, just once. Two thirds!

And here's why it works. Twelve is two times two times three. Eighteen is two times three times three. They share a two and a three. Two times three is six, the highest common factor.

Let's try one together. Simplify six eighths. What number divides both six and eight? Say your answer out loud!

Two divides both. Six divided by two is three. Eight divided by two is four. Three quarters! Well done if you said three quarters!

Your turn! Simplify twenty-four thirty-sixths. Pick the simplest card. You've got fifteen seconds, or pause the video. Go!

Time's up! The highest common factor is twelve. Twenty-four divided by twelve is two, and thirty-six divided by twelve is three. Two thirds! Four sixths is the same amount, but it isn't the simplest.

Quick review. Simplifying makes bigger pieces, but keeps the same amount. Divide the top and the bottom by the same number. And the highest common factor does it in one step. See you next time!