7.2 Ratios

To pin down this kind of comparison precisely, mathematics uses the idea of a ratio.

The ratio of width to height of poster A is written

80 : 60 \qquad (\text{read ``}80 \text{ to } 60\text{''}).

The numbers 80 and 60 are called the terms of the ratio.

What a Ratio Means In a ratio of the form a : b, for every a units of the first quantity there are b units of the second. So in poster A, for every 80 mm of width there are 60 mm of height.

The ratios of width to height for posters A, C and D are 80 : 60, \qquad 40 : 30, \qquad 120 : 90, and we saw that each can be obtained from another by multiplying both terms by the same factor. We call such ratios proportional. A reliable way to test this, without hunting for the factor each time, is to reduce every ratio to its simplest form and check whether the simplest forms match.

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