Proportion

A proportion is a statement of equality between two or more ratios. For example,

This proportion is read as, “3 is to 4 as 6 is to 8.”

Extremes and Means

The first and last terms of the proportion (the 3 and 8 in this example) are called the extremes. The second and third terms (the 4 and 6 in this example) are called the means. In any proportion, the product of the extremes is equal to the product of the means.

In the proportion 2:3 = 4:6, the product of the extremes, 2 × 6, is 12; the product of the means, 3 × 4, is also 12. An inspection of any proportion will show this to be true.

Solving Proportions

Normally when solving a proportion, three quantities will be known, and the fourth will be unknown. To solve for the unknown, multiply the two numbers along the diagonal and then divide by the third number.

Example: Solve for X in the proportion given below.

First, multiply 65 × 100: 65 × 100 = 6500

Next, divide by 80: 6500 ÷ 80 = 81.25

Therefore, X = 81.25.

Example: An airplane flying a distance of 300 miles used 24 gallons of gasoline. How many gallons will it need to travel 750 miles?

The ratio here is: “miles to gallons;” therefore, the proportion is set up as:

Therefore, to fly 750 miles, 60 gallons of gasoline will be required.

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