Simplifying ratios

Hello, and welcome to Myriora Maths! A class has twelve girls and eighteen boys. The ratio of girls to boys is twelve to eighteen. But we can write it in a much simpler way. Let's find out how.

Put the children into equal teams. Each team has two girls and three boys. There are six teams. So twelve to eighteen is the same as two to three.

Here's the quick way. Divide both numbers by the same number. Twelve and eighteen are both in the six times table. Twelve divided by six is two, and eighteen divided by six is three.

Use the biggest number that goes into both. That's the highest common factor, just like simplifying fractions. If you use a smaller one, like two, you get six to nine. That's not finished: divide by three again, and you get two to three.

It works for three parts too. Ten to fifteen to twenty-five: divide them all by five. That's two to three to five!

Let's try one together. Simplify eight to twelve. Say it out loud!

Four goes into eight and into twelve. Eight divided by four is two, and twelve divided by four is three. Two to three!

Here's a question that catches lots of people. Simplify six to nine. Some people take three away from both numbers, and get three to six. But taking away changes the ratio! Divide both by three instead: two to three.

Your turn! Simplify twenty to thirty-five. Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Five goes into twenty and into thirty-five. Twenty divided by five is four, and thirty-five divided by five is seven. Four to seven!

Quick review. To simplify a ratio, divide every part by the same number. Use the highest common factor, so it's done in one step. Never add or take away. And it works for three parts too. See you next time!