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

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.*

**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.

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