RATIO AND PROPORTION TUTORIAL

A ratio is a comparison of two quantities with the same units by division. The ratio of a to b can be written a/b, a:b, or a to b. In a ratio, the order of the terms is important. The number mentioned first is the numerator of the fraction, the number before the colon, or the number before the word to.

A ratio may express the relationship of a part to a whole, or it may express the relationship of a part to another part. Our study group can be used as an example. Our original group had 3 females and 1 male, so the relationship of one part to another part (females to males) would be 3 to 1. The relationship of one part to the whole (females to total number) would be 3 to 4.

A ratio should always be simplified, or reduced to lowest terms. For example, the ratio 3:15 should be reduced to 1:5.

A proportion is a mathematical statement showing that two ratios are equal. A proportion is written as an equation with a ratio on each side of the equal sign. For example, let’s say that a car can go 200 miles on 10 gallons of gas or 300 miles on 15 gallons of gas. This information can be written as a proportion: 200 mi/10 gal = 300 mi/15 gal.

When one of the terms of a proportion is unknown, we can “solve” the proportion for that term. The solution is the value of the unknown that makes the proportion true. Proportions can be solved using cross multiplication. Consider the car proportion above. If we want to know how far the car can go on 20 gallons of gas, we set up our proportion as follows: 200 mi/10 gal = x mi/20 gal

Cross multiply: (10)x = (200) (20) x = 400 mi