Write and Solve Proportions Lesson 6 Proportionality Write and Solve Proportions

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

Write and Solve Proportions Target: Write and solve proportions.

Vocabulary Proportion: An equation stating two ratios are equivalent.

Example 1a 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. ?

Example 1b 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. ? ?

Example 2a 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. ?

Example 2b 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. ?

Example 3 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

Exit Problems Solve each proportion. Determine whether the pair of ratios forms a proportion.

Communication Prompt How would a chef use proportions? How would a builder use proportions? How can you use proportions?