Proportions

Students learn that a proportion is a pair of equal ratios. For example, 2/4 = 3/6 is a proportion, because 2/4 and 3/6 are equal ratios. In the problems in this lesson, students are asked to determine if a given pair of ratios, such as 2/7 and 12/42, represents a proportion. The first step is to determine if the cross products of the ratios are equal. Note that the cross products of the ratios are the numerator of the first ratio times the denominator of the second ratio, and the denominator of the first ratio times the numerator of the second ratio. So for the ratios 2/7 and 12/42, the cross products are 2 x 42, or 84, and 7 x 12, or 84. Since the cross products are equal, the ratios are equal, which means that 2/7 and 12/42 form a proportion.