Lesson 8: 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

A recipe for sparkling grape juice calls for $1 \frac{1}{2}$ quarts of sparkling water and $\frac{3}{4}$ 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 punch?

Problem 3

Draw a scaled copy of the circle using a scale factor of 2.
How does the circumference of the scaled copy compare to the circumference of the original circle?
How does the area of the scaled copy compare to the area of the original circle?

Problem 4 From Unit 3 Lesson 6

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 5

Find each quotient.

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

Problem 6 From Unit 3 Lesson 6

Consider the problem: It takes one week for a crew of workers to pave $\frac{3}{5}$ 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.