Year 10 Interactive Maths - Second Edition

Ratios

A ratio is a comparison between two or more like quantities in the same units.

This suggests that a ratio can be simplified by dividing (or multiplying) its terms by the same number.

Note:

The ratio 1 : 2 is read as '1 to 2' or '1 is to 2'.

Simplification of Ratios

Example 1

Express the ratio 6 : 9 in its simplest form.

Solution:

Note:

The ratio 2 : 3 is in its simplest form since the numbers 2 and 3 have no common factor.

Scale Factor

If the ratio is expressed in the form 1 : n, then n is called the scale factor.

E.g.  10 : 100 = 1 : 10

So, 10 is the scale factor.

Equivalent Ratios

Clearly, 5 : 20 = 1 : 4

We say that 5 : 20 and 1 : 4 are equivalent.

In general:

Multiplying both terms of the ratio a : b by the same number, c, results in the equivalent ratio ac : bc.

Key Terms

ratio, terms of a ratio, simplest form of a ratio, scale factor, equivalent ratio