Ratio and proportion calculations

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Alternate method for solving percentage problems

Hospital Corpsman Revised Edition

Ratio Solutions

RATIO AND PROPORTION CALCULATIONS

Ratio is the relationship of one quantity to another quantity of like value. Example ratios are 5:2, 4:1. These ratios are expressed as "5 to 2" and "4 to 1," respectively. Aratio can exist only between values of the same kind, as the ratio of percent to percent, grams to grams, dollars to dollars. In other words, the denominator must be constant.

Proportion is two equal ratios considered simultaneously. An example proportion is

1:3::3:9
This proportion is expressed as "1 is to 3 as 3 is to 9." Since the ratios are equal, the proportion may also be written
1:3 = 3:9

Terms of Proportion
The first and fourth terms (the terms on the ends) are called the extremes. The second and third terms (middle terms) are called the means.

In a proportion, the product of the means equals the product of the extremes; therefore, when three terms are known, the fourth (or unknown) term may be determined.

Application of Proportion
The important factor when working proportions is to put the right values in the right places within the proportion. By following a few basic rules, you can accomplish this without difficulty and solve the problem correctly.

In numbering the four positions of a proportion from left to right (i.e., first, second, third, and fourth, observe the following rules):

Let X (the unknown value) always be in the fourth position.

Let the unit of like value to X be the third position.
If X is smaller than the third position, place the smaller of the two leftover values in the second position; if Xis larger, place the larger of the two values in the second position.

Place the last value in the first position. When the proportion is correctly placed, multiply the extremes and the means and determine the value of X, the unknown quantity.