Lesson 11: Practice Problems

Problem 1

Select all statements that show correct reasoning for finding $\frac{14}{15} \div \frac{7}{5}$ .

Multiplying $\frac{14}{15}$ by 5 and then by $\frac{1}{7}$ .
Dividing $\frac{14}{15}$ by 5, and then multiplying by $\frac{1}{7}$ .
Multiplying $\frac{14}{15}$ by 7, and then multiplying by $\frac{1}{5}$ .
Multiplying $\frac{14}{15}$ by 5 and then dividing by 7.
Multiplying $\frac{15}{14}$ by 7 and then dividing by 5.

Problem 2

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

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

Problem 3

Find the value of $\frac{15}{4} \div \frac{5}{8}$ . Show your reasoning.

Problem 4

Kiran has $2 \frac{3}{4}$ pounds of flour. When he divides the flour into equal-sized bags, he fills $4 \frac{1}{8}$ bags. How many pounds fit in each bag?

Write a multiplication equation and a division equation to represent the question and then answer the question. Show your reasoning.

Problem 5 From Unit 4 Lesson 10

Divide $4 \frac{1}{2}$ by the following unit fractions.

$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{6}$

Problem 6 From Unit 4 Lesson 9

After charging for $\frac{1}{3}$ of an hour, a phone is at $\frac{2}{5}$ of its full power. How long will it take the phone to charge completely?

Decide whether each equation can represent the situation.

$\frac{1}{3} \cdot ? = \frac{2}{5}$
$\frac{1}{3} \div \frac{2}{5} = ?$
$\frac{2}{5} \div \frac{1}{3} = ?$
$\frac{2}{5} \cdot ? = \frac{1}{3}$

Problem 7 From Unit 4 Lesson 8

Elena and Noah are each filling a bucket with water. Noah’s bucket is $\frac{2}{5}$ full and the water weighs $2 \frac{1}{2}$ pounds. How much does Elena’s bucket weigh if her bucket is full and her bucket is identical to Noah’s?

Write multiplication and division equations to represent the question.
Draw a diagram to show the relationship between the quantities and to answer the question.