Fractions as ratios

Ratios are most commonly used to express the quantitative relationship between two groups, and can be modelled using discrete items.

For example, the ratio of 2 to 3 can be represented as a group of two squares compared to a group of three triangles:

Ratio of 2 to 3.

This can be expressed as 2:3 or as \(\frac{2}{3}\).

Another way of describing a ratio is that it indicates the number of times one amount contains the other amount, or is contained within the other amount. We could say that:

• the group of squares is \(\frac{2}{3}\) the size of the group of triangles, or
• the group of triangles is \(\frac{3}{2}\) the size of the group of squares.

Rate is also an expression of a ratio, but is usually used in more dynamic contexts. Rate is often used to describe a constant relationship in the increase or decrease of measures, such as time or length.