Working with Ratio

Working with Ratio

Join us as we share the educational wealth with this concise post focusing on ‘Working with Ratio’ and ‘Sharing an Amount in a Given Ratio’.

You’ll find contextual overviews and step-by-step breakdowns of worked examples that should help you refresh or establish your knowledge in the topic.

Let’s get started!

Writing Ratios

Ratios are used as a way to divide an amount into different shares. We write a ratio with numbers (representing the size of each share) separated by colons.

For example, 

Working with ratio - 2:3, red:blue counter example.

The ratio of red counters to blue counters is 2:3. This is read as “2 to 3”. 

This means that for every 2 red counters, we have 3 blue counters. 

Remember that order matters. If we wrote 3:2, that would mean that for every 3 red counters, we have 2 blue counters. 

Simplifying Ratios 

If each number in a ratio has a common factor, we can simplify that ratio. We do this by dividing each number by the highest common factor. 

Make sure that the units match before doing this. 

Working with Ratio – Worked Examples

Example 1 

Simplify 10:15. 

Both 10 and 15 are divisible by 5. 

  • 10 ÷ 5 = 2 
  • 15 ÷ 5 = 3 

The answer is 2:3

Example 2 

Simplify 20:36:16 

The highest common factor might not be instantly obvious so look for any common factor. We could begin by dividing by 2 to get 10:18:8 

We can see that each number can be divided by 2 again. 

The answer is 5:9:4


Try Beyond Maths’s Working with Ratio Walkthrough Worksheet for a printable PDF copy that’s ideal for taught lessons, independent study or home learning.

Working with Ratio KS3 Walkthrough Worksheet

Sharing an Amount in a Given Ratio

The most straightforward example of sharing in a ratio is when you are told the amount that needs sharing and given the relevant ratio. 

There are three steps: 

  • 1. Add the parts of the ratio together. 
  • 2. Divide the total amount by this number. 
  • 3. Multiply the original numbers in the ratio by this new value. 

For example, 

Share £80 in the ratio 1:4. 

1. Add the parts of the ratio together. 

  • 1 + 4 = 5 
  • This tells us that we are sharing £80 into 5 parts

2. Divide £80 by 5. 

  • 80 ÷ 5 = £16 
  • This tells us that 1 part of our ratio is worth £16

3. Multiply the numbers in the ratio by £16. 

  • 1 × 16 = £16 
  • 4 × 16 = £64 
  • We can check the answers by making sure that they add up to the original amount.

Sharing is caring so why not Share an Amount in a Given Ratio with this Walkthrough Worksheet?

Sharing an Amount in a Given Ratio KS3 Walkthrough Worksheet

Check your understanding of the content above by trying out these tasks.

Ratio Questions

1. Simplify the following ratios:

  • a) 4:10
  • b) 21:14
  • c) 9:12
  • d) 50:20
  • e) 3:9:6
  • f) 20:35:15

2. A shelter contains 8 cats and 20 dogs. Write the ratio of cats to dogs, giving your answer in its simplest form.

3. A box contains blue sweets and orange sweets. There are 30 sweets altogether. 6 of the sweets are blue. Write the ratio of blue sweets to orange sweets in its simplest form.

4. Share each amount in the given ratio.

  • a) £40 in the ratio 1:3
  • b) £20 in the ratio 2:3
  • c) £56 in the ratio 2:5
  • d) 24p in the ratio 5:3

5. Alex is 5 years old and Becky is 7. They are going to share £60 in the ratio of their ages. Work out how much each child gets.

6. A box contains 120 sweets. Ali, Billy and Caleb share the sweets in the ratio 4:7:1. Work out how many more sweets Billy receives than Ali.

Answers

1a) 2:5     b) 3:2     c) 3:4     d) 5:2     e) 1:3:2     f) 4:7:3

2. 2:5

3. 1:4

4a) 10:30     b) 8:12     c) 16:40     d) 15:9

5. £25 for Alex; £35 for Becky

6. Billy receives 30 sweets more than Ali.


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