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§ 2.7

Ratios and Proportions. § 2.7. 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.). Ratios.

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§ 2.7

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  1. Ratios and Proportions § 2.7

  2. A ratiois 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.) Ratios

  3. means extremes Proportions A proportionis a statement of equality between two ratios. a and d are the extremes; b and c are the means

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

  5. Solving with Proportions • Understand the problem. • Translate the problem into mathematical language by representing the unknown by a variable and setting up the proportion. • Solve the proportion. • Check your answer. • Make sure you have answered the question.

  6. 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? Unknown Given ratio Given quantity Solving with Proportions Answer: Let x = number of gallons 1(5775) = 825x (Cross multiply.) 7 = x (Divide by 825.) 7 gallons are needed.

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