The amount of numbers in a ratio tell us how many people we are sharing an amount between.

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.