ProportionalityWrite and Solve Proportions

Lesson 6

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?

Warm-Up

Write and Solve ProportionsTarget:

Write and solve proportions.

Proportion: An equation stating two ratios are equivalent.

Vocabulary

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 1a

153

2 x

15

10

3

2?

15

10

3

2

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 1b

7

5.16

a

a

5.1

28

6?

76)28(5.1 ?

4242

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 2a

6

2 and

9

4

6

2

9

4?

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 2b

30

50 and

9

15

30

50

9

15?

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

Example 3

minutes 45

$

minutes 30

4$ b

Solve each proportion.

1.

2.

Determine whether the pair of ratios forms a proportion.

3.

4.

Exit Problems

315

25 x

a

8

9

6

12

10 and

5

4

10

6 and

15

9

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

Communication Prompt