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Chapter 6 Percent © 2010 Pearson Education, Inc. All rights reserved. 6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem Objectives 1. Learn the percent proportion. 2. Solve for an unknown value in a percent proportion. 3. Identify the percent. 4. Identify the whole. 5. Identify the part. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 2 The percent proportion can be used to solve problems. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 3 Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. a. part = 20, percent = 80; find the whole. p a rt w h o le p a rt 20 w h o le x p e rce n t 100 80 p e rce n t 100 100 Find the cross products. 20 x Show that the cross products are equivalent. 80 100 x • 80 20 • 100 80 x 20 100 80 x 2000 x 25 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 4 Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. b. part = 12, whole = 40; find the percent. p a rt w h o le p a rt 12 w h o le 40 3 10 p e rce n t 100 x p e rce n t 100 100 x Write the fraction in lowest terms. 100 10 x 3 100 Find the cross products. 10 x 300 Divide both sides by 10. x 30 The percent is written as 30%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 5 Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. c. whole = 120, percent = 90; find the part. p a rt p e rce n t w h o le 100 p a rt x w h o le 120 90 p e rce n t 100 100 x 120 9 10 Write the fraction in lowest terms. 10 x 9 120 Find the cross products. 10 x 1080 Divide both sides by 10. x 108 The part is 108. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 6 Percent Problems All percent problems involve a comparison between a part of something and the whole. Percent The percent is the ratio of a part to a whole, with 100 as the denominator. In a problem, the percent appears with the word percent or with the symbol “%” after it. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 7 Parallel Example 2 Finding the Percent in Percent Problems Find the percent in the following. a. 20% of the 740 customers were children. Percent b. $90 is what 40 percent of what number? Percent c. What percent of 320 is 272? Percent (unknown) Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 8 Whole The whole is the entire quantity. In a percent problem, the whole often appears after the word of. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 9 Parallel Example 3 Finding the Whole in Percent Problems Find the whole in the following. a. 14% of 600 cars were convertibles. Whole b. $200 is 30 percent of what number? Whole c. 70% of 8220 is what number? Whole Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 10 Part The part is the portion being compared with the whole. Note: If you have trouble identifying the part, find the percent and the whole first. The remaining number is the part. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 11 Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) a. 60% of 450 animals is 270 animals. Percent; with % sign Whole Part Whole Part 270 450 60 100 Percent Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 12 Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) b. $240 is 10% of what number? Part Percent Part Whole Whole (unknown) 240 u n kn o w n 10 100 Percent Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 13 Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) c. 35% of 600 is what number? Percent Whole Part Whole Part (unknown) unknow n 600 35 100 Percent Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 6.3- 14