Dividing a Quantity in a Given Ratio

The term “dividing a quantity in a given ratio” is just another way of saying we’re splitting something, such as money, sweets, or even time, into parts according to a specific rule or proportion.

Before we look at it in more detail, let’s quickly revisit what a ratio is. A ratio is a simple way to compare two or more values. For example, if you and a friend share a bag of 12 sweets in a 3:1 ratio, you’d get three times as many sweets as your friend.

Dividing a quantity in a given ratio requires three main steps:

1. Setting up the problem

2. Adding up the total parts

3. Dividing the quantity

Setting up the Problem

Whenever you’re faced with a problem of dividing a quantity in a given ratio, the first step is to understand the total quantity that you have and how you need to divide it.

For example, if you’re sharing £60 between you and a friend in a ratio of 3:2, the total quantity is £60, and the ratio is 3:2.

Adding up the Total parts

The next step is to add up the total parts. You can do this by adding all the numbers in the ratio together.

In our example of £60 in a 3:2 ratio, you’d add 3 + 2 to get 5. This common factor tells us how many parts the total quantity will be divided into.

Dividing the Quantity

Now comes the division. To find out how much each of you will get, you’ll divide the total quantity (£60) by the common factor (5). \pounds 60 \div 5 = \pounds 12.

Then, you multiply this answer by each part of the ratio to find out how much each person gets. You’ll get 3 \times \pounds 12 = \pounds 36 and your friend will get 2 \times \pounds 12 = \pounds 24.

Practice Questions

Question 1:

Divide £40 in a 2:3 ratio.

Add 2+3 = 52+3 = 5

Then, \pounds 40 \div 5 = \pounds 8\pounds 40 \div 5 = \pounds 8

Now, \pounds 8 \times 2 = \pounds 16\pounds 8 \times 2 = \pounds 16 and \pounds 8 \times 3 = \pounds 24\pounds 8 \times 3 = \pounds 24


Question 2:

Share 30 sweets in a 4:1 ratio.

Add 4+1 = 54+1 = 5

Then, 30 \div 5 = 630 \div 5 = 6

Now, 6 \times 4 = 246 \times 4 = 24 and 6 \times 1 = 66 \times 1 = 6


Question 3:

Divide £100 in a 5:2:3 ratio.

Add 5+2+3 = 105+2+3 = 10. Then, \pounds 100 \div 10 = \pounds 10\pounds 100 \div 10 = \pounds 10

Now, \pounds 10 \times 5 = \pounds 50\pounds 10 \times 5 = \pounds 50, \pounds 10 \times 2 = \pounds 20\pounds 10 \times 2 = \pounds 20, and \pounds 10 \times 3 = \pounds 30\pounds 10 \times 3 = \pounds 30


Question 4:

Share 50 sweets in a 2:2:1 ratio.

Add 2+2+1 = 52+2+1 = 5

Then, 50 \div 5 = 1050 \div 5 = 10

Now, 10 \times 2 = 2010 \times 2 = 20, 10 \times 2 = 2010 \times 2 = 20, and 10 \times 1 = 1010 \times 1 = 10

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