Proportion Definition

In this section, we learn how to determine if two ratios or two rates represent a proportion. We start with determining if two fractions are equal in value. To do this, we utilize a procedure known as the "equality test for fractions". This tells us that if two fractions are equal in value, their cross products must be equal. What are cross products? Cross products occur when we multiply across fractions, the denominator of one fraction is multiplied by the numerator of the other.
Example 1: Find the cross products $$\frac{3}{5}, \frac{1}{2}$$ • Multiply 2 x 3 = 6
• Multiply 5 x 1 = 5
The cross products here are 6 and 5.
Once we have mastered this concept, we apply the same logic to working with ratios and rates. To determine if two ratios or two rates represent a proportion, we simply check to see if their cross products are equal. We only think about the number parts, we do not look at the units. In the case of a rate, we must ensure that the same units are in the numerator and denominator of each.
Example 2: Determine if the following represents a proportion $$\frac{2}{3}=\frac{6}{9}$$ • The cross products are: 3 x 6 = 18 and 9 x 2 = 18
Since the cross products are equal, we do have a proportion.