Question

unit comparing quantities

Answer 1

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 8 : 12 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.



So, 10 is the scale factor.


Equivalent Ratios



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