Ratios

A ratio is simply a way to compare two or more quantities. It helps you understand the relationship between those quantities. For example, the amount of orange squash you mix in per litre of water or comparing the number of boys to girls in your classroom.

Ratios can be written in different ways, but the most common method is using a colon. For example, if there are 2 apples and 3 oranges in a basket, the ratio of apples to oranges is written as 2:3.

Note that the order is important here, 2:3 is not the same as 3:2. The first number in the ratio always relates to the first item you’re talking about, and the second number relates to the second item.

Two important skills are knowing how to:

• Simplify ratios

• Compare equivalent ratios

Let’s look at both briefly.

Simplifying Ratios

Just like you can simplify fractions, you can also simplify ratios. For example, let’s look at the ratio 4:6. Both numbers are divisible by 2, so if you divide each by 2, you’ll get a simplified ratio of 2:3.

Simplifying ratios helps to make them easier to work with and understand.

Equivalent Ratios

Once you’ve got a grip on simplifying ratios, the next thing to know is that ratios can be equivalent. For example, the ratio 2:3 is equivalent to 4:6, 6:9 and 8:12.

You find these by multiplying or dividing both parts of the ratio by the same number.

Practice Questions

Question 1:

Simplify the ratio 10:15

Solution

Both 10 and 15 can be divided by 5.

So, and

The simplified ratio is 2:3

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Question 2:

The ratio of red to blue marbles in a bag is 2:3. If there are 10 red marbles, how many blue marbles are there?

Solution

The ratio is 2:3, and we know that there are 10 red marbles. To find the number of blue marbles, we set it up like this: 2 is to 3 as 10 is to what?

Solving for x gives , which gives

So, there are 15 blue marbles.

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Question 3:

In a class, the ratio of boys to girls is 3:5. If there are 12 boys, how many students are there in total?

Solution

The ratio of boys to girls is 3:5, so for every 3 boys, there are 5 girls.

If there are 12 boys, then girls.

The total number of students would be students.