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5.01 Working with ratios

Lesson

Ratios

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

One blue dot and 3 green dots.

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.

5 circles and 14 squares.
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.

Idea summary

A ratio compares the relationship between two values. We write ratios in the form a:b which is read as "a to b".

Convert between units

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

Example 2

Write 31 minutes to 2 hours as a ratio.

Worked Solution
Create a strategy

Convert the hours to minutes and express the similar quantities as a ratio.

Apply the idea

1 hour =60 minutes

\displaystyle \text{Minutes}\displaystyle =\displaystyle 2 \times 60Multiply the hours by 60
\displaystyle =\displaystyle 120 \text{ min}Evaluate the product

We can write the ratio of 31 minutes to 120 minutes as 31:120.

Idea summary

To compare quantities with different units, we need to convert one of the quantities to the same units as the other. Then we can write it in the form a:b without units.

Outcomes

VCMNA249

Recognise and solve problems involving simple ratios

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