# Lesson 8

Ratios and Rates With Fractions

### Problem 1

Clare said that $$\frac{4}{3}\div\frac52$$ is $$\frac{10}{3}$$. She reasoned: $$\frac{4}{3} \boldcdot 5=\frac{20}{3}$$ and $$\frac{20}{3}\div 2=\frac{10}{3}$$

Explain why Clare’s answer and reasoning are incorrect. Find the correct quotient.

### Solution

(From Unit 3, Lesson 7.)

### Problem 2

A recipe for sparkling grape juice calls for $$1\frac12$$ quarts of sparkling water and $$\frac34$$ quart of grape juice.

1. How much sparkling water would you need to mix with 9 quarts of grape juice?
2. How much grape juice would you need to mix with $$\frac{15}{4}$$ quarts of sparkling water?
3. How much of each ingredient would you need to make 100 quarts of sparkling grape juice?

### Problem 3

At a deli counter,

• Someone bought $$1 \frac34$$ pounds of ham for $14.50. • Someone bought $$2 \frac12$$ pounds of turkey for$26.25.
• Someone bought $$\frac38$$ pounds of roast beef for \$5.50.

Which meat is the least expensive per pound? Which meat is the most expensive per pound? Explain how you know.

### Problem 4

Consider the problem: After charging for $$\frac13$$ of an hour, a phone is at $$\frac25$$ of its full power. How long will it take the phone to charge completely?

Decide whether each equation can represent the situation.

1. $$\frac13\boldcdot {?}=\frac25$$
2. $$\frac13\div \frac25={?}$$
3. $$\frac25 \div \frac13 ={?}$$
4. $$\frac25 \boldcdot {?}=\frac13$$

### Solution

(From Unit 3, Lesson 6.)

### Problem 5

Find each quotient.

1. $$5 \div \frac{1}{10}$$
2. $$5 \div \frac{3}{10}$$
3. $$5\div \frac{9}{10}$$

### Solution

(From Unit 3, Lesson 7.)

### Problem 6

Consider the problem: It takes one week for a crew of workers to pave $$\frac35$$ kilometer of a road. At that rate, how long will it take to pave 1 kilometer?

Write a multiplication equation and a division equation to represent the question. Then find the answer and show your reasoning.