Year 8 Interactive Maths - Second Edition

Comparing Quantities

This suggests that a ratio can be simplified by dividing its terms by the same number.  Therefore:

This suggests that the terms of a ratio can be multiplied by the same number.  Therefore:

Note:

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

Simplifying Ratios

Example 1

Express the ratio 30 : 42 in its simplest form.

Solution:

Note:

The ratio 5 : 7 is in its simplest form since the numbers 5 and 7 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.  5 : 20 = 1 : 4
So, 4 is the scale factor.

Equivalent Ratios

Clearly 18 : 27 = 2 : 3

We say that:

18 : 27 and 2 : 3 are equivalent.

Key Terms

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