Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 6 Ratio, Proportion, and Percent

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 6.1 Ratio and Proportion

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. A ratio is the quotient of two quantities. Writing Ratios as Fractions For example, a percent can be thought of as a ratio, since it is the quotient of a number and % = or the ratio of 53 to 100

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The ratio of a number a to a number b is their quotient. Ways of writing ratios are and a b a to b,a : b, Ratio

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. A proportion is a statement that two ratios are equal. Solving Proportions If and are two ratios, then is a proportion. a b c d a b c d =

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Proportions A proportion contains four numbers. If any three numbers are known, the fourth number can be found by solving the proportion. To solve use cross products. a b c d a b c d = Multiply both sides by the LCD, bd Simplify ad = bc cross product ad bc These are called cross products.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Proportions are True ? True proportion

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Unknown Numbers in Proportions Cross multiply. Simplify the left side. Divide both sides by 28. Check:

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. A 16-oz Cinnamon Mocha Iced Tea at a local coffee shop has 80 calories. How many calories are there in a 28-oz Cinnamon Mocha Iced Tea? Solving Problems by Writing Proportions Solve the proportion. Cross multiply. Simplify the right side. Divide both side by 140. A 28-oz Cinnamon Mocha Iced Tea has 140 calories.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. When writing proportions to solve problems, write the proportions so that the numerators have the same unit measures and the denominators have the same unit measures. For example, Helpful Hint