Arithmetic : Ratio and Proportion

Ratio

A ratio is a number (like a fraction) that compares two numbers by division.
The ratio of a to b may be written in different ways such as a to b, or a : b, or a ÷ b, or a / b.
The numbers a and b are called the terms of the ratio.

Since a ratio a : b is a fraction a / b, the term b cannot be zero.
Ratios can be treated just like fractions.
Since the fraction a / b is different from the fraction b / a, the order of the terms in a ratio is important.
For example, the ratio of the number of sides in a pentagon to the number of sides in an octagon is 5 : 8 and not 8 : 5.

To find the ratio of two quantities, they must be expressed in the same unit of measure.

Example
What is the ratio of 5 feet to 9 inches?
Solution. click here for solution

Note that a division of two distinct quantities with different units is usually a rate and not a ratio.
For example, 100 miles / 2 hours is a rate of speed of 50 miles per hour.