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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, simplest
form, scale factor, equivalent ratio |
