§ 2.7

Ratios and Proportions

Angel, Elementary Algebra, 7ed 2

Ratios

A A ratio is a quotient of two quantities. Ratios is a quotient of two quantities. Ratios provide a way to compare two numbers. provide a way to compare two numbers. They may be written as:They may be written as:

a a to to b,b, aa::b,b, or or ba

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.)

.26 13 4 2

Angel, Elementary Algebra, 7ed 3

Proportions

A proportion is a statement of equality between two ratios.

dc

ba

extremes

meansmeans

a and d are the extremes;

b and c are the means

Angel, Elementary Algebra, 7ed 4

Cross-Multiplication

If , then ad = bc.dc

ba

(Note that the product of the means equals the product of the extremes.)

Example: Since then 1·10 = 2·5.1 5

2 10,

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.

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Solving with ProportionsExample: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

feet 5775gallons

feet 825gallon 1 xGiven ratio

Unknown

Given quantity

1(5775) = 825x (Cross multiply.)

7 = x (Divide by 825.)

7 gallons are needed.