# Lesson video

In progress...

Hi, I'm Mrs Dennett.

And in this lesson, we're going to be learning about how to simplify ratios.

To simplify a ratio, we must find the highest common factor of the parts involved.

The highest common factor of 15 and 20 is five.

So we divide 15 and 20 by five, to get three to four.

To simplify 42 to 154.

We again find the highest common factor, the highest common factor of 42 and 154 is 14.

So divide each part by 14 to get three to 11.

Sometimes we have to simplify ratios that include units of measurement, such as length, time and weight.

Before we simplify these ratios, we must make sure that each part of the ratio is written using the same units.

Here, one metre is a hundred centimetres, so we change one metre to a hundred centimetres, and then both 50 and 100 have the same units.

The both written in centimetres.

Find the highest common factor, which is 50 and divide by it.

So we get one to two.

To simplify one hour to 10 minutes, change the hour to 60 minutes.

We now have 60 minutes to 10 minutes, the same units.

Find the highest common factor and divide by it.

So divided by 10 gives us six to one.

Here, we have a box which contains 40 red bags, 28 blue bags and 64 green bags.

We want to write the ratio of red to blue to green bags in its simplest form.

In this ratio, there are three parts red to blue to green.

So we have 40 to 28 to 64.

Make sure you get them in the correct order.

We find the highest common factor of all three numbers.

The highest common factor of 40, 28 and 64 is four.

So we divide each part of the ratio by four, and we get 10 to seven to 16.

Here's some questions for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers, I won't go through all of them, but let's have a look at part d, 36 to 48.

You may not have spotted straight away that the highest common factor of 36 and 48 is 12.

You could instead divide by a common factor first.

So may be divided by four to get nine to 12, and then find the highest common factor of these two numbers, which is three, divided by three gives us three to four.

There are more steps involved in this, but common factors may be easier for you to spot, you'll know when you have the ratio in its simplest form, because the parts will not have any more common factors.

Here is question to you to try, remember to make the units the same before you simplify the ratios.

Pause the video to complete the task and restart when you were finished, Here are the answers.

For this question, you may have needed to recap some units of measure.

So for part a, you needed to know that one kilogramme is a thousand grammes.

The part b, you need to know that there are 24 hours in a day.

So we end up simplifying six hours to 24 hours.

And for c, there are 60 seconds in a minute, 18 times 60 is 1080.

So we end up simplifying 1,080 to 100 divided by their highest common factor, which is 20.

In question three, we can use multiplication to help us to find equivalent ratios.

Multiplying by two gives eight to 14, multiply by three, gives us 12 to 21, and so on.

As long as you multiply each part, by the same number, you will always find an equivalent ratio.

Here's some questions for you to try.

Pause the video to complete the task and restart when you were finished.

For these questions, you just need to make sure that you put the ratios in the correct order.

This order is given in the question.

So you must write children to teachers, 120 to 20, and then simplify, not teachers to children.

Here is a final question for you to try.

Pause the video to complete this question and restart when you're finished.

The length is longer than the width.

So we simplify 15 to six, both in metres.

So we just divide each part by their highest common factor, which is three.

For part b, we have to first find the perimeter of the rectangle.

Notice that some of the side lengths are missing, but we know about opposite side lengths in a rectangle are the same.