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.


(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. \(\frac25 \boldcdot {?}=\frac13\)
(From Unit 3, Lesson 6.)

Problem 5

Find each quotient.

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

(From Unit 3, Lesson 6.)