1. Write and Solve Proportions
Lesson 6
Proportionality
Write and Solve Proportions

2. 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?

3. Write and Solve Proportions
Target:
Write and solve proportions.

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

6. Example 1a Solve the proportion using cross products.
Write the cross products ·x = 2·15
Simplify the equation x = 30
Divide both sides by x = 10
Check your answer.
simplifies to , so the solution is correct. ?

7. Example 1b Solve the proportion using cross products.
Write the cross products ·a = 6·7
Simplify the equation a = 42
Divide both sides by a = 28
Check your answer. ? ?

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

9. Example 2b Determine whether the pair of ratios forms a proportion.
Write the proportion using ≟.
Check using cross products ·30 ≟ 9·50
Simplify ≟ 450
The cross products are equal so the ratios form a proportion. ?

10. 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 ·45 = 30·b
Simplify = 30b
Divide both sides by = b
$6 in 45 minutes

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

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