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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.

If we compare 5 cm with 10 cm as a ratio, we write 5 : 10 or 5/10.  We call 5 and 10 the terms of the ratio.

We know that 5/10 = 1/2.

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

5 : 10 = 1 : 2

Also 1/2 = 5/10

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

1 : 2 = 5 : 10


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.

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.


Key Terms

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


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