1. § 2.7 Ratios and Proportions

2. Angel, Elementary Algebra, 7ed 2 Ratios A is a quotient of two quantities. Ratios provide a way to compare two numbers. They may be written as: A ratio is a quotient of two quantities. Ratios provide a way to compare two numbers. They may be written as: a to b,a:b, or Example: The ratio of 26 ounces to 4 pounds could be written as (It may also be written as 13 to 2 or 13:2.)

3. Angel, Elementary Algebra, 7ed 3 Proportions A proportion is a statement of equality between two ratios. extremes means a and d are the extremes; b and c are the means

4. Angel, Elementary Algebra, 7ed 4 Cross-Multiplication If, then ad = bc. (Note that the product of the means equals the product of the extremes.) Example: Since then 1·10 = 2·5.

5. Angel, Elementary Algebra, 7ed 5 Solving with Proportions 1.Understand the problem. 2.Translate the problem into mathematical language by representing the unknown by a variable and setting up the proportion. 3.Solve the proportion. 4.Check your answer. 5.Make sure you have answered the question.

6. Angel, Elementary Algebra, 7ed 6 Solving with Proportions Example: A gallon of paint covers 825 square feet. How much paint is needed to cover a house with a surface area of 5775 square feet? Answer: Let x = number of gallons Given ratio Unknown Given quantity 1(5775) = 825x (Cross multiply.) 7 = x (Divide by 825.) 7 gallons are needed.