1. § 3.2 Ratio and Proportion

2. A ratio compares quantities by division. The ratio of a to b can be expressed as a:b or Ratio Blitzer, Introductory Algebra, 5e – Slide #2 Section 3.2

3. Example: In a class, there are 15 girls and 20 boys. Find the ratio of boys to girls. The ratio of boys to girls is 4 to 3 or 4:3. Ratio Blitzer, Introductory Algebra, 5e – Slide #3 Section 3.2

4. A proportion is a statement that says two ratios are equal. Proportions Blitzer, Introductory Algebra, 5e – Slide #4 Section 3.2

5. Cross Product Principal for Proportions The cross products ad and bc are equal. Solving Proportions Blitzer, Introductory Algebra, 5e – Slide #5 Section 3.2

6. Example: Solve the proportion: 3(x + 3) = 2(6)Cross multiply. 3x + 9 = 12Distribute. 3x = 3Subtract 9 from both sides. x = 1Divide both sides by 3. Solving Proportions Blitzer, Introductory Algebra, 5e – Slide #6 Section 3.2

7. Solving Applied Problems Using Proportions 1.Read the problem and represent the unknown quantity by x (or any letter). 2.Set up a proportion by listing the given ratio on one side and the ratio with the unknown quantity on the other side. Each respective quantity should occupy the same corresponding position on each side of the proportion. 3.Drop units and apply the cross-products principle. 4.Solve for x and answer the question. Applied Problems Blitzer, Introductory Algebra, 5e – Slide #7 Section 3.2

8. Example: If the gas bill for an apartment with 800 square feet is $45, how much would you expect the bill to be for a 1000 square foot apartment? 1.Represent the unknown. x = gas bill for 1000 square foot apartment 2.Set up the proportion. Using Proportions Blitzer, Introductory Algebra, 5e – Slide #8 Section 3.2

9. Example: If the gas bill for an apartment with 800 square feet is $45, how much would you expect the bill to be for a 1000 square foot apartment? 3.Drop the units and apply the cross-products principle. 800x = 45(1000)Cross-product. 800x = 45000Multiply. 4.Solve for x and answer the question. x = 56.25Divide both sides by 800. The gas bill for the 1000 square feet apartment should be $56.25. Using Proportions, Continued Blitzer, Introductory Algebra, 5e – Slide #9 Section 3.2

10. Of importance to note… Blitzer, Introductory Algebra, 5e – Slide #10 Section 3.2 A ratio compares quantities by division. A ratio is usually written as a simple fraction. A proportion is a statement or an equation that compares ratios. A proportion says that two ratios are equal. To solve a proportion, we use the Cross-Products Principle for Proportions.