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Ratios are used in concentration of solutions, drug dosages, similar
figures, gearing, mechanical advantage and debt versus capital finance. Similar figures
are widely used in the building industry, and knowledge of
ratios is essential to understand the concept of similar figures.
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 of a ratio, simplest
form of a ratio, scale factor, equivalent
ratio
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