# 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,

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

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.

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.

## 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?

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.

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 and £30     b) £8 and £12     c) £16 and £40     d) £15 and £9

5. £25 for Alex; £35 for Becky

6. Billy receives 30 sweets more than Ali.

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## 2 thoughts on “Working with Ratio”

1. Aisha says:

I didn’t like how the answer of the example was written differently than the answer in the practice question in sharing ratio. Example question answer:£64. Practice questions answer: 10:30,8:12… The inconsistency is very confusing.

1. damianbullock says:

Hi there 👋 Thanks for commenting and pointing out the differences. We’ve edited the post now so that the answers for the practice questions match the consistencies used in the example answers. I hope this helps! Enjoy your day 🙂