# Lesson 8

Ratios and Rates With Fractions

Let’s calculate some 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.

### Problem 2

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

- How much sparkling water would you need to mix with 9 quarts of grape juice?
- How much grape juice would you need to mix with \(\frac{15}{4}\) quarts of sparkling water?
- 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.

- \(\frac13\boldcdot {?}=\frac25\)
- \(\frac13\div \frac25={?}\)
- \(\frac25 \div \frac13 ={?}\)
- \(\frac25 \boldcdot {?}=\frac13\)

### Problem 5

Find each quotient.

- \(5 \div \frac{1}{10}\)
- \(5 \div \frac{3}{10}\)
- \(5\div \frac{9}{10}\)

### 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.