Comparing Quantities

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Year 7 Interactive Maths - Second Edition

Comparing Quantities

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

Compare AB to CD.

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

5 : 10 = 1 : 2

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

A ratio a : b (or a/b) is said to be its simplest form if a : b (or a/b) has been reduced to its lowest terms. That is, a and b have no common factor.

Example 1

Express the ratio 8 : 12 in its simplest form.

Solution:

By dividing both terms by 4, we find 8 : 12 = 2 : 3

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.

So, 10 is the scale factor.

Equivalent Ratios

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

Key Terms

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

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