DEFINITIONS
When given two ratios (in the form x:y) or two relations (in the form of fractions), if the ratios of each element are the same they're said to be proportionate.
Example: 3/6 and 1/2 are proportionate because 3 out 6 is the same as 1 out of two (half).
PROVING PROPORTIONALITY
When given two fractions to prove as proportionate, such as
1 | and | 3 | |
2 | 6 |
you solve through cross-multiplication.
Cross multiplication involves multiplying the numerator (number on top) by the denominator (number on bottom) of the other fraction, and then comparing the results. If the values are the same, the fractions are proportionate.
The set-up above will be set-up as such:
1 * 6 | ? | 2 * 3 |
(6) | = | (6). |
Because both values are the same, these fractions are proportionate.
Example 2:
3/2 | and | 18/8 |
The cross-multiplication yields:
3 * 8 | ? | 18 * 2 |
24 | ? | 36 |
Because 24 does not equal 36, these two fractions are not proportionate.
Example 3:
6/10 | and | 9/15 |
The cross-multiplication yields:
6 * 15 | ? | 9 * 10 |
90 | = | 90 |
Since both multiplications solve as 90, these two fractions are proportionate.