Ratio and Proportion
After reviewing this chapter, you should be able to:
1. Define ratio and proportion
3. Calculate problems for a missing term (x) using ratio and proportion
RATIOS
A ratio is used to indicate a relationship between two numbers. These numbers are separated by a colon (:).
PROPORTIONS
A proportion is an equation of two ratios of equal value. The terms of the first ratio have a relationship to the terms of the second ratio. A proportion can be written in any of the following formats:
Example:
The terms in a proportion are called the means and extremes. Confusion of these terms can result in an incorrect answer. To avoid confusion of terms in proportions, remember m for the middle terms (means) and e for the end terms (extremes) of the proportion. Let’s refer to our example to identify these terms.
The extremes are the outer or end numbers (previous example: 5, 50), and the means are the inner or middle numbers (previous example: 25, 10).
Example:
To verify that the two ratios in a proportion are equal and that the proportion is true, multiply the numerator of each ratio by its opposite denominator. The products should be equal. The numerator of the first fraction and the denominator of the second fraction are the extremes. The numerator of the second fraction and the denominator of the first fraction are the means.
SOLVING FOR x IN RATIO AND PROPORTION
Because the product of the means always equals the product of the extremes, if three numbers of the two ratios are known, the fourth number can be found. The unknown quantity may be any of the four terms. In a proportion problem, the unknown quantity is represented by x. After multiplying the means and extremes, the unknown x is usually placed on the left side of the equation. Begin with the product containing the x that will result in the x being isolated on the left and the answer on the right.
Steps:
