Chapter 2 Section 6

Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Ratio, Proportion, and Percent Write ratios. Solve proportions. Solve applied problems by using proportions. Find percents and percentages

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Write ratios. Slide 2.6-3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. A ratio is a comparison of two quantities using a quotient. The last way of writing a ratio is most common in algebra. Ratio The ratio of the number a to the number b (b ≠ 0) is written or Slide Write ratios.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write a ratio for each word phrase. 3 days to 2 weeks 12 hr to 4 days Solution: Slide EXAMPLE 1 Writing Word Phrases as Ratios

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The 36 oz. size is the best buy. The unit price is $0.108 per oz. The supermarket charges the following prices for pancake syrup. Which size is the best buy? What is the unit cost for that size? Slide EXAMPLE 2 Finding Price per Unit

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Solve proportions. Slide 2.6-7

Copyright © 2012, 2008, 2004 Pearson Education, Inc. A ratio is used to compare two numbers or amounts. A proportion says that two ratios are equal, so it is a special type of equation. For example, is a proportion which says that the ratios and are equal. In the proportion a, b, c, and d are the terms of the proportion. The terms a and d are called the extremes, and the terms b and c are called the means. We read the proportions as “a is to b as c is to d.” Slide Solve proportions.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. We can also find the products ad and bc by multiplying diagonally. For this reason, ad and bc are called cross products. Beginning with this proportion and multiplying each side by the common denominator, bd, gives Slide Solve proportions. (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Cross Products If then the cross products ad and bc are equal—that is, the product of the extremes equals the product of the means. Also, if then Slide Solve proportions. (cont’d) If then ad = cb, or ad = bc. This means that the two proportions are equivalent, and the proportion can also be written as Sometimes one form is more convenient to work with than the other.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: False Solution: True Decide whether the proportion is true or false. Slide EXAMPLE 3 Deciding Whether Proportions Are True

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The solution set is {5}. The cross-product method cannot be used directly if there is more than one term on either side of the equals symbol. Solve the proportion Slide EXAMPLE 4 Finding an Unknown in a Proportion

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The solution set is When you set cross products equal to each other, you are really multiplying each ratio in the proportion by a common denominator. Solve Slide EXAMPLE 5 Solving an Equation by Using Cross Products

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Solve applied problems by using proportions. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Let x = the price of 16.5 gal of fuel gal of diesel fuel costs $ Twelve gallons of diesel fuel costs $ How much would 16.5 gal of the same fuel cost? Slide EXAMPLE 6 Applying Proportions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 4 Find percents and percentages. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. A percent is a ratio where the second number is always 100. Since the word percent means “per 100,” one percent means “one per one hundred.” or Slide Write ratios.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Convert. 310% to a decimal 8% to a decimal to a percent Solution: 3.1 Slide EXAMPLE 7 Converting Between Decimals and Percents %

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve each problem. What is 6% of 80? 16% of what number is 12? What percent of 75 is 90? Solution: Slide EXAMPLE 8 Solving Percent Equations

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Let x = the number of possible points on the test. There were 40 possible points on the test. Mark scored 34 points on a test, which was 85% of the possible points. How many possible points were on the test? Slide EXAMPLE 9 Solving Applied Percent Problems