Lesson 8

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.

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?

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.

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. $\frac25 \boldcdot {?}=\frac13$

Find each quotient.

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

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.