Section 3 3 Proportions VOCABULARY Proportion an equation

Section 3. 3 Proportions

VOCABULARY Proportion: an equation stating that two ratios are equivalent Example: 6 cokes = 12 cokes $3 $6 Proportional: when two quantities form a proportion In the example above, since the price of 1 coke is 50 cents in either ratio, they are said to be proportional.

Determining if Two Ratios form a Proportion Two determine if two proportions are proportional or form a proportion check their cross-products. If their cross products are equal, the ratios are proportional. If the cross products are not equal, the ratios ARE NOT proportional. ? ? 1 = 7 1 x 21 = 3 x 7 3 21 21 = 21 Since the cross products are equal, yes, these ratios form a proportion. Example 1: Do the ratios form a proportion? Example 2: Do the two rates form a proportion? 12 players from 21 teams; 15 players from 24 teams? ? ? 12 players = 15 players 12 x 24 = 21 x 15 21 teams 24 teams 288 ≠ 315 Since the cross products are not equal, no, these rates do not form a proportion. Notice that in the first ratio players is on the top and teams are on the bottom. The next ratio is set up the same way. It is important that however you set the first ratio up, you set the second ratio up identical!!

THE LAST ONE!!!!! Example 3: You read the first 20 pages of your book in 25 minutes. You read the next 36 pages in 45 minutes. Is the number of pages you read proportional to your time? ? ? Does 20 x 45 = 25 x 36? 20 pages = 36 pages 900 = 900 25 min. 45 min. Since the cross products are equal the ratios are proportional.