1. Write and Solve Proportions Lesson 6

2. 1. Ten boys and 15 girls ran a mile under seven minutes in P.E. a)Write the ratio of boys to girls who ran a mile under seven minutes. b)Write the ratio of boys to all students who ran a mile under seven minutes. c)Write the ratio of girls to all students who ran a mile under seven minutes. 2. The football team had a win to loss ratio of 5 : 2. What is their ratio of wins to total games played?

3. Target: Write and solve proportions.

5.  Proportion: An equation stating two ratios are equivalent.

6. Solve the proportion using cross products.  Write the cross products. 3·x = 2·15  Simplify the equation. 3x = 30  Divide both sides by 3. x = 10  Check your answer.  simplifies to, so the solution is correct. ?

7. Solve the proportion using cross products.  Write the cross products. 1.5·a = 6·7  Simplify the equation. 1.5a = 42  Divide both sides by 1.5. a = 28  Check your answer. ? ?

8. Determine whether the pair of ratios forms a proportion.  Write the proportion using ≟.  Check using cross products. 4·6 ≟ 9·2  Simplify. 24 ≟ 18  24 18 so the ratios DO NOT form a proportion. ?

9. Determine whether the pair of ratios forms a proportion.  Write the proportion using ≟.  Check using cross products. 15·30 ≟ 9·50  Simplify. 450 ≟ 450  The cross products are equal so the ratios form a proportion. ?

10. Write a proportion for the following phrase and solve it: $4 in 30 minutes; $b in 45 minutes.  Write both ratios with dollars in numerator and minutes in denominator.  Write the cross products. 4·45 = 30·b  Simplify. 180 = 30b  Divide both sides by 30. 6 = b  $6 in 45 minutes

11. Solve each proportion. 1. 2. Determine whether the pair of ratios forms a proportion. 3. 4.

12. How would a chef use proportions? How would a builder use proportions? How can you use proportions?