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 making incense sticks calls for 6 tablespoons of joss powder, \(1\frac12\) teaspoons of frankincense, and \(\frac34\) teaspoon of myrrh. To make incense sticks that would smell the same, how much of the other two ingredients would you need to mix with:

1. 4 tablespoons of joss powder?
2. 9 tablespoons of joss powder?
3. 1 teaspoon of myrrh?

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 \(\frac38\) pound 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.

A phone’s battery is out of power. After charging for \(\frac{1}{3}\) of an hour, the battery is at \(\frac{2}{5}\) of its full power. How long (in total) will it take the battery 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.