Ratio, Proportion and Rates

Ratios can be used to compare the quantities of same type of objects and of different types. There are 2 types of ratios which compare quantities of the same type. When the comparison is to part of the whole to the other part of the whole, then the ratio is a part-part ratio. Two other related concepts, rate and proportion, together with the ratio, are used for the solving real-world problems which involve comparing different quantities.

In a unit rate, denominator quantity is 1. A unit rate is used for comparing cost of 2 similar items.

When 2 ratios are equal, mathematical statement of that equality is known as proportion.

If a/b is equal to c/d, then a/b = c/d is known as proportion. To find out if 2 ratios form a proportion, one can evaluate the cross product. If a/b and c/d are ratios, then the 2 ratios form a proportion if ad = bc.

Proportions are used when 3 quantities are given, and the 4th quantity is an unknown.

A ratio compares the magnitude of 2 quantities. When the quantities have different units, then a ratio is known as rate. A proportion is a statement of equality among 2 ratios.

A ratio is the comparison of 2 numbers. We generally separate the 2 numbers in the ratio with a colon (:).To compare ratios, write them in the forms fractions. The ratios are equal if they are equal when given by fractions.

When 1 of the 4 numbers in a proportion is unknown, cross products can be used to find the unknown number. This is called as solving the proportion.

A rate is a ratio which expresses how long it takes to do something, like traveling a certain distance. To walk 3 kilometers in 1 hour is to walk at the rate of 3 km/h. The fraction expressing a rate has units of distance in numerator and units of time in denominator.
Problems involving rates involve setting 2 ratios equal to each other and solving for an unknown quantity that is, solving a proportion.

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