Chapter 2 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Ratios and Proportions Write ratios. Solve proportions. Solve applied problems by using proportions.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Slide Write ratios.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write ratios. A ratio is a comparison of two quantities using a quotient. The last way of writing a ratio is most common in algebra. Percents are ratios in which the second number is always 100. For example, 50% represents the ratio 50 to 100, 27% represents the ratio 27 to 100, and so on. Slide The ratio of the number a to the number b (b ≠ 0) is written or
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write a ratio for each word phrase. 3 days to 2 weeks 12 hr to 4 days EXAMPLE 1 Writing Word Phrases as Ratios Solution: Slide
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Solution: Finding Price per Unit The 36 oz. size is the best buy. The unit price is $0.108 per oz. Slide The local supermarket charges the following prices for a popular brand of pancake syrup. Which size is the best buy? What is the unit cost for that size?
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Solve proportions. Slide
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve proportions. Slide 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.”
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Beginning with this proportion and multiplying each side by the common denominator, bd, gives Solve proportions. (cont’d) We can also find the products ad and bc by multiplying diagonally. For this reason, ad and bc are called cross products. Slide
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve proportions. (cont’d) Slide If then the cross products ad and bc are equal. Also, if then From this rule, if then ad = bc; that is, the product of the extremes equals the product of the means. 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 © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Solution: False Deciding whether Proportions Are True Slide Solution: True Decide whether the proportion is true or false.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Solution: Finding an Unknown in a Proportion Slide 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.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 The solution set is Solving an Equation by Using Cross Products Slide Solution: When you set cross products equal to each other, you are really multiplying each ratio in the proportion by a common denominator. Solve
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Solve applied problems with proportions. Slide
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Solution: Let x = the price of 16.5 gal of fuel. Applying Proportions Slide gal of diesel fuel costs $ Twelve gal of diesel fuel costs $ How much would 16.5 gal of the same fuel cost?