Ratio, Proportion and Rates

Ratios can be used to compare quantities of the same type of objects and of different types. There are two types of ratios that compare quantities of the same type. When the comparison is to part of the whole to the whole, then the ratio is a part-whole ratio. When the comparison is to part of the whole to another part of the whole, then the ratio is a part-part ratio. Two other related concepts, rate and proportion, together with ratio, are used for solving many real-world problems that involve comparing different quantities.

In a unit rate, the denominator quantity is 1. A unit rate is often used for comparing the cost of two similar items.

When two ratios are equal, the mathematical statement of that equality is called a proportion.

If a/b is equal to c/d  , then a/b = c/d is called a proportion. To find out if two ratios form a proportion, one can evaluate the cross product. If and are ratios, then the two ratios form a proportion if ad = bc.

Proportions are used when three quantities are given, and the fourth quantity is an unknown.

A ratio compares the magnitude of two quantities. When the quantities have different units, then a ratio is called a rate. A proportion is a statement of equality between two ratios.

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:).To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion.

A rate is a ratio that expresses how long it takes to do something, such as traveling a certain distance. To walk 3 kilometers in one hour is to walk at the rate of 3 km/h. The fraction expressing a rate has units of distance in the numerator and units of time in the denominator. Problems involving rates typically involve setting two ratios equal to each other and solving for an unknown quantity that is, solving a proportion.