TABLE OF CONTENTS Ratios and proportions appear in many practical applications of mathematics. They are used to express relationships between two or more quantities.
A ratio is a division relationship that expresses a statement of comparison between two quantities of the same units, such as ft/ft, lb/lb, or of different units, such as $/hour, feet/second, or miles/gallon. The slash symbol (/) stands for per in discussions of ratios or proportions. It also indicates rate, and again, rate and ratio both involve division. Hence, the ratio of quantity a to quantity b can be expressed as a/b or 
, the common fraction of a divided by b. A ratio can also be expressed with a colon (:). Thus a : b is also the ratio of a to b.
A ratio is a fraction.
Because a ratio is a fraction, all rules for fractions apply to ratios as well. For example, suppose the ratio of an adult s height to a child s height is 6:4. This ratio can be reduced to 3:2, or it can be expressed as the fraction 6/4, with the reduced form 3/2 being the preferred form. Thus, a ratio might be an improper fraction, such as 3/2, or it might be a proper fraction, such as 2/3. In the latter case we would be expressing the ratio of the child s height to the adult s height.
The statement, One hammer weighs...
