Out of the two ways of comparing the magnitudes of two numbers, subtraction and division, only the latter is relevant for describing proportions.
Rates remain the same regardless of their units, e.g.:
3 hours to 2 hours
9 metres to 6 metres
108° to 72°
Numbers are proportionate when fractions are equal:
Given a sequence of
Since the numbers are in a continued proportion they are all multiples of the same number .
Given , and such that
is the mean proportional between and . Therefore
Other Theorems on Proportions
since multiplying by the LCD yields
and the and cancel, it follows that
- If two fractions are equal, so are their reciprocals
- Another pair of proportional fractions can be made by rearranging the fractions
Manipulation With a Common Value