1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 2 Equations, Inequalities, and Applications Chapter 2

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 3 2.6 Ratio, Proportion, and Percent

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 4 Objectives 1.Write ratios. 2.Solve proportions. 3.Solve applied problems using proportions. 4.Find percentages and percents. 2.6 Ratio, Proportion, and Percent

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 5 Writing Ratios Ratio A ratio is a comparison of two quantities using a quotient. The ratio of the number a to the number b is written a to b,a : b, or. a b 2.6 Ratio, Proportion, and Percent

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 6 (a) The ratio of 7 yards to 4 yards is Writing Ratios (b) To find the ratio of 8 feet to 6 yards, first convert 6 yards to feet. 7 4 7 yd 4 yd =. 6 yards = 6 3 = 18 ft 4 9 8 ft 18 ft =. 8 ft 6 yd = The ratio of 8 feet to 6 yards is thus Example 1 Write a ratio for each word phrase. 2.6 Ratio, Proportion, and Percent

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 7 SizePrice 18-oz$1.89 40-oz$4.16 64-oz$7.04 Writing Ratios Example 2 What size is the best buy? That is, which size has the lowest unit price? PEANUT BUTTER 2.6 Ratio, Proportion, and Percent

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 8 Writing Ratios Example 2 (continued) SizePriceUnit Cost (dollars per ounce) 18-oz$1.89 40-oz$4.16 64-oz$7.04 $1.89 18 $4.16 40 $7.04 64 = $0.105 = $0.104 = $0.110 Best Buy! Because the 40-oz size produces the lowest unit cost, it is the best buy. 2.6 Ratio, Proportion, and Percent

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 9 Solving Proportions a b c d = If, then ad and bc are equal and are called cross products. A proportion says that two ratios are equal, so it is a special type of equation. We read the proportion a b c d = (b, d ≠ 0). as “a is to b as c is to d.” We can also find the products ad and bc by multiplying diagonally. 2.6 Ratio, Proportion, and Percent

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 10 Solving Proportions Cross products must be equal. Example 3 Solve the proportion. 2 3 x 51 = 2 3 x = 2 51 = 3 x Multiply.102 = 3x Divide by 3.34 = x Check by substituting 34 for x in the proportion. The solution is 34. 2.6 Ratio, Proportion, and Percent

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 11 Solving Proportions Cross products must be equal.6 ( w – 4 ) = 3 ( w + 1 ) 3w = 27 Divide by 3.w = 9 Check that the solution is 9. Example 4 Solve the equation. = w – 4 3 w + 1 6 = w – 4 3 w + 1 6 6w – 24 = 3w + 3Distribute. Add 24.6w = 3w + 27 Subtract 3w. 2.6 Ratio, Proportion, and Percent

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 12 Solving Applied Problems Using Proportions Cross products must be equal.15.33x = 7.0(35.04) He pumped a total of 16 gal. Check this answer. Notice that the way the proportion is set up uses the fact that the unit price is the same, no matter how the gallons are purchased. = $15.33 7.0 $35.04 x 15.33x = 245.28Multiply. Divide.x = 16 Example 5 After Edwin pumped 7.0 gal of gasoline, the display showing the price read $15.33. When he finished pumping the gasoline, the display read $35.04. How many gallons did he pump? Price Gallons 2.6 Ratio, Proportion, and Percent

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 13 Finding Percentages and Percents We can solve a percent problem by writing it as a proportion a b P 100 = The amount, or percentage, is compared to the base (the whole amount). Since percent means per 100, we compare the numerical value of the percent to 100. amount base percent 100 = or. 2.6 Ratio, Proportion, and Percent

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 14 Finding Percentages and Percents Cross products must be equal.100a = 750(16) Thus, 16% of 750 is 120. 100a = 12,000Multiply. Divide.a = 120 Example 6 Find 16% of 750. a b P 100 = a 750 16 100 = 2.6 Ratio, Proportion, and Percent

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 15 Finding Percentages and Percents Cross products must be equal.100a = 15(26) The amount of the discount on the CD is $3.90, and the sale price is $15.00 – $3.90 = $11.10. 100a = 390Multiply. Divide.a = 3.90 Example 7 A CD with a regular price of $15 is on sale this week at 26% off. Find the amount of the discount and the sale price this week. a b P 100 = a 15 26 100 = 2.6 Ratio, Proportion, and Percent

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 16 Finding Percentages and Percents Cross products must be equal.100(255) = 850P The sale price represented a 30% savings. 25,500 = 850PMultiply. Divide.30 = P Example 8 A computer advertisement was listed in the newspaper for $595. The regular price was $850. What percent of the regular price was the savings? a b P 100 = 255 850 P 100 = The savings amounted to $850 – $595 = $255. 2.6 Ratio, Proportion, and Percent