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Year 8 Interactive Maths - Second Edition


Comparing Quantities

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 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


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