5.01 Working with ratios

A ratio compares the relationship between two values. It tells us how much there is of one thing compared to another.

If we want to describe the relationship between the number of blue dots and the number of green dots, we could say that there is 3 blue dot for every 1 green dots. We could also express this as a ratio, which we would write as 1:3.

It is important that both quantities are in the same units, otherwise we cannot compare them with a ratio. In the example above, we are comparing one blue dot to three green dots, so a single dot can be thought of as our unit.

A ratio can express a "part to part" relationship like we saw in the dot example above. We can also describe a "part to whole relationship". For example, if we wanted to describe the ratio of green dots to all the dots, we could write it as 3:4, because there are 3 green dots and 4 dots in total.

The order that the words are written correspond to the order of the values in the ratio, so it is important that we don't jumble them around. We can also express fractions, decimals and percentages as ratios.

Examples

Example 1

Write a numerical ratio for the number of circles to squares. Give your answer in the form a:b.

Worked Solution

Create a strategy

Count the number of circles and squares. Write the ratio as the number of circles to squares.

Apply the idea

There are 5 circles and 14 squares. We can write the ratio as 5:14.

Watch question walkthrough

Often we might want to compare two quantities that have different units, such as a number of minutes compared to a number of hours, a distance in kilometres to a distance in metres, a duration in days to a duration in weeks, and so on.

To compare these types of quantities, we will need to convert one of the quantities to use the same units as the other. It does not matter which one we convert, we will end up with exactly the same ratio in the end.

Examples