KS2

Solving problems with ratio

Part ofMathsRatioYear 6

What is ratio?

Showing the form in which ratio is written a:b.

A ratio shows how much of one thing there is compared to another.

Ratios are a way to represent proportion.

Ratios are usually written in the form a:b. For example 5:1

Showing the form in which ratio is written a:b.

Activity: How to solve problems using ratio

Complete this interactive activity to understand how to use ratio to solve problems. Then test your knowledge.

Example 1

There are 6 cupcakes in a batch - 4 chocolate cupcakes and 2 strawberry cupcakes.

The ratio of chocolate to strawberry cupcakes is 4:2.

This ratio tells us that for every four chocolate cupcakes, there are two strawberry cupcakes.

How many strawberry cupcakes will there be, if there were 24 chocolate cupcakes?

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You know the ratio of chocolate to strawberry cupcakes is 4:2.
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You can visualise a ratio using a bar model. It looks like this.
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We can write this in a ratio table.
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You need to work out how many times the number 4 (from the ratio) has been multiplied to get to 24.
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To find this, divide 24 by 4: 24 ÷ 4 = 6. This tells us that the ratio part for chocolate cupcakes has been multiplied by 6 to get to 24.
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Since the ratio of chocolate to strawberry cupcakes is 4:2, we need to multiply the number of strawberry cupcakes in the ratio by the same number. 2 x 6 = 12.
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So, if you have 24 chocolate cupcakes, you will have 12 strawberry cupcakes.

Example 2

You have a pencil case filled with coloured pencils.

For every 3 blue pencils, you have 2 red pencils. If you have 18 blue pencils, how many red pencils do you have?

How can you scale up the ratio of blue to red pencils?

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First, write the ratio of blue pencils to red pencils. The ratio is 3:2.
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To scale up a ratio, you have to multiply both numbers by the same factor. You can use a ratio grid to help.
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What number have you multiplied 3 by to get 18? 3 x 6 = 18
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So you have to multiply the number of red pencils by the same number. For the red pencils: 2 × 6 = 12
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So, the scaled-up ratio of blue pencils to red pencils is 18:12. This means that if you have 18 blue pencils, you will have 12 red pencils.

Example 3

You are making a fruit salad. The recipe says you must follow a ratio of apples to oranges.

The ratio is 3:2.

This means for every 3 apples, you need 2 oranges.

You have 9 apples to use. How many oranges will you need to keep the same ratio?

Skip image gallery

Image caption,
First, write the ratio of apples to oranges. The ratio is 3:2. To scale up a ratio, you have to multiply both numbers by the same factor.
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You can use a ratio grid to help. What number have you multiplied 3 by to get 9 apples? 3 × 3 = 9
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So, you have to multiply the number of oranges by the same number. For the oranges: 2 × 3 = 6
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So, the scaled-up ratio of apples to oranges is 9:6
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This means that if you use 9 apples, you will need 6 oranges to keep the same ratio of 3:2.

Example 4

At sports club, the coach has to order balls in sets.

Each set contains 5 footballs and 4 netballs.

The coach wants to order 5 more sets of balls.

How many footballs and netballs will the club have in total?

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First, write the ratio of footballs to netballs in each set. The ratio is 5:4.
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Next, work out the number of footballs and netballs in one set: 5 footballs 4 netballs
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The coach wants to order 5 more sets. So there will be 6 sets in total. To scale up the ratio, multiply both numbers by the total number of sets. Let's use a ratio grid to help.
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So, you have to multiply the number of footballs and netballs by the same number. For the footballs: 5 × 6 = 30 For the netballs: 4 × 6 = 24.
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So, the total number of footballs and netballs will be 30 + 24, which is 54 balls.

More on Ratio

Find out more by working through a topic

Converting between ratios, fractions and percentages
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Using scale factors
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