1. 9.1 Ratios and Proportions

2. You will learn to use ratios and proportions to solve problems. 1) ratio 2) proportion 3) cross products 4) extremes 5) means

3. In 2000, about 180 million tons of solid waste was created in the United States. The paper made up about 72 million tons of this waste. The ratio of paper waste to total waste is 72 to 180. This ratio can be written in the following ways. 72 to 18072:18072 ÷ 180 Definition of Ratio A ratio is a comparison of two numbers by division. a to ba:ba ÷ b where b  0

4. A __________ is an equation that shows two equivalent ratios. proportion Every proportion has two cross products. In the proportion to the right, the terms 20 and 3 are called the extremes, and the terms 30 and 2 are called the means. The cross products are 20(3) and 30(2). The cross products are always _____ in a proportion. equal 30(2) =20(3) 60 = 60

5. Theorem 9-1 Property of Proportions For any numbers a and c and any nonzero numbers b and d, Likewise,

6. Solve each proportion: 15(2x) =30(6) 30x = 180 x = 6 3(x) =(30 – x)2 3x = 60 – 2x 5x = 60 x = 12

7. The gear ratio is the number of teeth on the driving gear to the number of teeth on the driven gear. Driving gear Driven gear If the gear ratio is 5:2 and the driving gear has 35 teeth, how many teeth does the driven gear have? given ratio equivalent ratio = 5 2 35 x = driving gear driven gear driving gear driven gear 5 x = 70 x = 14 The driven gear has 14 teeth.