A ratio indicates how much of one thing there is in proportion to another, or how many times one number can fit into another. Ratios behave much like fractions and can be simplified.

When we work out ratios, if we have a value assigned to the whole it can then be divided in proportion to the given ratio.

As a basic example, say you saw a statistic suggesting that the number of women working somewhere outnumbered men, in a ratio of 5:2. If you knew how many people in total worked for the company, then using the ratio given to you, it is easy to work out the number of men and number of women (since for every two men there are five women).

There are many other occasions where you may be required to work out ratios and divide them. For instance, when working with data, or with scale, and of course, when answering questions in numerical reasoning tests.

## A step-by-step guide to dividing ratios

When dividing ratios, we are essentially dividing a whole number into a number of smaller numbers and assigning those in proportion to the specified ratio by multiplying.

To divide a ratio, follow the steps below.

## Step 1: Find the sum of the ratio's values

Using the example above, we are trying to work out how many men work at a company if men and women are employed on a 2:5 ratio. We know that there are 49 people at the company.

The first step is to add the parts of the ratio together: 2 + 5 = 7.

## Step 2: Divide by the sum of the ratio

We then divide the total number of people working at the company (49) by the sum of the ratio’s value which we got in step one.

So 49 / 7 = 7

This gives what is called a quotient of 7.

## Step 3: Multiply with the quotient

Divide the amount into the given ratio. Multiply each of the ratio values with the quotient (the number we got in step 2). So 49 divided up into the ratio of 2:5, we get:

2 x 7 = 14

5 x 7 = 35

(35 + 14 = 49)

## Example questions

Below are some questions for you to try out yourself.

While the method for dividing ratios is relatively simple in theory, it does become more complex when working with larger figures.

### Example question 1

Mo was given £1,500 to buy clothes for his new job as well as an armchair for his new apartment. He decided to spend at a ratio of 2:3, with the greater sum to be spent on his new wardrobe. How much was his armchair budget?

We start by finding the sum of the ratio value (2:3). This is the simple addition of 2 + 3 = 5.

We then take the total that Mo was given, which was £1,500, and divide that by the 5 that we got at step one. So £1,500 / 5 = £300. This gives a quotient of 300.

We then need to multiply the ratio value by the quotient. So, in this case, we know he spends the lesser sum on the armchair, so we take the 2 (rather than the 3) and multiply them together.

300 x 2 = 600. Mo, therefore, had a budget of £600 to spend on his armchair.

### Example question 2

Harriet is planning to give her three staff members a bonus relating to how long they have worked in the business. She has an available budget of £3,900.

The amount will be divided in the ratio of 1:2:3, with the newest member of staff receiving the least amount. How much would each of the staff members receive?

We first find the sum of the ratio value (1:2:3). This is the simple addition of 1 + 2 + 3 = 6.

We then take the total that Harriet has available (£3,900), which we divide by the 6 that we got at step one. So £3,900 / 6 = £650. This gives a quotient of 650.

We then need to multiply the ratio value by the quotient.

The newest member of staff is easy as they only get one share, so they get £650.

The next member of staff gets £650 x 2 = £1,300.

The longest-serving member of staff gets £650 x 3 = £1,950.

Then check the working (650 + 1,300 + 1950 = 3,900).