Lesson 3 - Ratios

Lesson 3 - Ratios

Learning intentions - Be able to use ratios correctly

• Bronze - To be able to simplify ratios.

• Silver - To be able to split an amount into a ratio.

• Gold - To be able to find unknowns with ratios.

What are ratios?

Have a watch of the video to give yourself a recap on what ratios are.

Simplifying ratios

When simplifying ratios, you will need to first make sure that they are in the same units.

On the image to the right, you can see that the first step is to alter the units from 0.5m to 50cm.

The second step is then to divide both sides by the largest number possible to still leave whole numbers.

In the example, this would be dividing by 5 to leave a ratio of 3:10.

Multiple Choice

What is the ratio of fish to sharks?

• 8:2

• 10:2

• 2:8

Ratio of fish to sharks

• Because fish are asked for first, the answer should be 8:2

• This could have been simplified to 4:1, but lets start easy!

Multiple Choice

If there are 88 students for 4 classes
How many students should there be per class?

• 22 students per class
• 22 classes per student
• 25 students per class
• 25 classes per student

88 students for 4 classes

• To find the ratio, you need should look at the ratio as 88:4.

• Both of these can be divided by 4 to give 22:1.

• This would mean there should be 22 students per class.

Multiple Choice

A class has 15 boys and 20 girls. What is the boy:girl ratio in simplest form?

• 4 : 5
• 10 : 13
• 3:4
• 3:5

Ratio of boys and girls

• With 15 boys and 20 girls, the ratio is 15:20.

• Both of these can be divided by 5 to leave you with the simplest ratio of 3:4

Simplify the ratio 1m:40cm

• This is a tricky one! First you have to make the units the same. We could therefore say it as 100cm:40cm.

• Both of these figures can be divided by 20.

• Doing this will give us the simplest ratio of 5:2.

Splitting ratios

Splitting ratios can be difficult but you should be able to work through it.

In the question on the right, you need to split £35 in the ratio 3:4. The first step is to add the ratio amounts together which gives you 7.

If you then use this figure to divide the amount to be shared which is £35, you should see that each 1 is equal to £5.

Each ratio then needs to be multiplied by this figure which would be 2 x £5 to give £15 and 4 x £5 to give £20.

Splitting ratios

Still need help splitting ratios? Check out this video for further support before giving a go on the questions next.

Multiple Choice

You want a new TV. It is £350. Your flatmate offers to pay for more than half, splitting the cost with you in the ratio 3:2. How much do they have to pay?

• £150
• £210
• £200
• £300

Splitting the cost - £350 in a 3:2 ratio

• As discussed before, you would need to add together the two ratios of 3 and 2 to get 5.

• You would then divide £350 by 5 to give a value of £70 per unit.

• If these are then multiplied by the ratio amounts, we should get the figure of £210:£140

• Because your flatmate offered to pay more, their figure is £210.

Multiple Choice

Hana shares some of her money in a ratio 3:1 with Mark? She has £1 million to share. How much will she give Mark?

• £600,000

• £400,000

• £250,000

• £200,000

Sharing £1 million with Mark 3:1

• As before, you need to add together the ratio amounts of 3:1 to give you 4.

• If you then use this to divide £1 million, you should be able to figure our that each unit is worth £250,000.

• This can then be multiplied by the ratios to give a split of £750,000:£250,000

• This means that Mark would get £250,000.

Finding unknowns with ratios

Sometimes, you will need to work out values using ratios in a problem solving method. Look at the picture on the right. How would you go about working this out?

Finding unknowns with ratios

• To work this out, you first need to figure out a value that you can compare the coffee - we will use 100ml in this instance.

• To figure this out, we can divide the large by 5 to give a value of 50p:100ml, divide the medium by 2 to give a value of 49p:100ml and the multiply the small by 2.5 to give a value of 95p:100ml.

• We can then compare these to see that the best value for money is the medium at 49p:100ml.

Solving ratios

Still not sure on ratios? Have a watch of the following video to see it again!

Multiple Choice

Using the image, which size is better value for money?

• Large

• Standard

Which size is better value for money?

To get them to a point where you can compare them, you could multiply the standard jar by 2. This would give you a value of £2.78:500ml.

This compared to the large at £2.69:500ml should show that the LARGE is better value for money.

When do we use ratios in real life?

• You may find yourself cooking meals and using a recipe that is intended for 4 people, but you might want to alter it and make it for 8.

• To do so, all of the original ingredients would need to be altered to make enough for everyone. To keep to the ratio 1:4, you might then need to alter your amounts!

• Look at the questions on the right to see what you might need to take into consideration when making smoothies.

Exit ticket!

Fantastic work! Be sure to head over to your Microsoft Teams page for Maths and find the Microsoft Forms quiz on the 'assignments' tab. 

If you complete this quiz, that will act as your register for this session. No completed quiz - no mark!