
- 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.
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.