- There are three numbers in the ratio: ‘2’, ‘5’ and ‘3’. This means that the amount is shared between three people.
- 2 + 5 + 3 equals a total of 10 parts in the ratio.
- To find the value of each part, we divide the amount of £20 by the total number of parts.
- £20 ÷ 10 = £2.
- Finally we multiply each of the three numbers in our ratio by the value of each part.
- 2:5:3 multiplied by £2 gives the final answer of £4:£10:£6.

**The value of each part is found by dividing the given amount by the sum of the parts in the ratio.**

**We then multiply each number in the ratio by the value of each part.**

- We are sharing $48 between three people in the ratio 3:1:2.
- The total number of parts in the ratio is 3 + 1 + 2 = 6 parts.
- To find the value of each part in the ratio we divide $48 by the total number of parts.
- $48 ÷ 6 = $8.
- To find how much each person receives we multiply the ratio by the value of each part.
- 13:1:2 multiplied by $8 is $24:$8:$16.
- The first person receives $24, the second person receives $8 and the third person receives $16.

#### Calculating a Ratio of 3 Numbers: Interactive Questions

#### Sharing in a Ratio of 3 Numbers: Worksheets and Answers

# How to Calculate Ratios of 3 Numbers

In this lesson we will be looking at calculating ratios that contain 3 numbers and so, we will be sharing a given amount between three people.

To calculate a ratio of 3 numbers, we follow 3 steps:

**Step 1:**Find the total number of parts in the ratio by adding the numbers in the ratio together**Step 2:**Find the value of each part in the ratio by dividing the given amount by the total number of parts.**Step 3:**Multiply the original ratio by the value of each part

Here is our first example of calculating a ratio of three numbers:

We are asked to share **$48** between three people in the ratio **3:1:2**.

This means that for every **three parts** a person receives, a second person is given **one part** and a third person is given **two parts**.

We will work out how much money each person receives by following the three steps.

**Step 1: Find the total number of parts.**

Looking at the ratio **3:1:2**, we have:

3 + 1 + 2 = 6

So, **six parts in total**.

**Step 2: Divide the given amount by the total number of parts in the ratio.**

The amount is **$48** and the **total number of parts is 6**.

48 ÷ 6 = 8

**Each part in the ratio is worth $8**.

**Step 3: Multiply each number in the ratio by the value of one part.**

We will **multiply** each number in the ratio 3:1:2 **by $8**.

3 x $8 = $24

1 x $8 = $8

2 x $8 = $16

The money is shared in the ratio **$24:$8:$16**.

The first person receives $24, the second person receives $8 and the third person receives $16.

Having calculated this ratio of three numbers, we can check our result by adding the values together. $24 + $8 + $16 = $48, which is the total amount that we started with.

We can also check our result by simplifying the ratio 24:8:16.

All of these numbers are in the eight times table and dividing them by 8, we get back to our original ratio of 3:1:2.

Now try our lesson on *Finding the Mean* where we learn how to find the mean of a set of numbers.