Ratios

Ratios
Ratios tell how one number is related to another number.

A ratio may be written as A:B or A/B or by the phrase "A to B".

A ratio of 1:5 says that the second number is five times as large as the first.

The following steps will allow determination of a number when one number and the ratio between the numbers is given.

Example: Determine the value of B if A=6 and the ratio of A:B = 2:5

* Determine how many times the number A is divisible by the corresponding portion of the ratio. (6/2=3)
* Multiply this number by the portion of the ratio representing B (3*5=15)
* Therefore if the ratio of A:B is 2:5 and A=6 then B=15

How to Determine a Ratio

Ratios represent how one quantity is related to another quantity.

A ratio may be written as A:B or A/B or by the phrase "A to B".

A ratio of 1:5 says that the second quantity is five times as large as the first.

The following steps will allow a ratio to be determination if two numbers are known.

Example: Determine the ratio of 24 to 40.

* Divide both terms of the ratio by the greatest common factor (24/8 = 3, 40/8=5)
* State the ratio. (The ratio of 24 to 40 is 3:5)


Cross multiplication to solve proportions

A proportion is an equation which states that two ratios are equal.

When the terms of a proportion are cross multiplied, the cross products are equal.

Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.

21 3
-- = --
70 10


21 * 10 = 70 * 3


210 = 210

If one term of a proportion is not known, cross multiplication can be used to find the value of that term.

x 3
-- = --
70 10


x * 10 = 70 * 3


10x = 210


10x 210
--- = ---
10 10


x = 21


Unit Rates

A rate is a ratio that is used to compare different kinds of quantities.

A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Some common unit rates are miles (or kilometers) per hour, cost per item, earnings per week, etc. In each case the first quantity is related to 1 unit of the second quantity.