Lesson 10: Practice Problems

Problem 1

Priya is sharing 24 apples equally with some friends. She uses division to determine how many people can have a share if each person gets a particular number of apples. For example, $24 \div 4 = 6$ means that if each person gets 4 apples, 6 people can have apples. Here are some other calculations:

$24 \div 4 = 6$

$24 \div 2 = 12$

$24 \div 1 = 24$

$24 \div \frac{1}{2} = ?$

Priya thinks the “?” represents a number less than 24. Do you agree? Explain or show your reasoning.
In the case of $24 \div \frac{1}{2} = ?$ , how many people can have apples?

Problem 2

Here is a centimeter ruler.

Use the ruler to find $1 \div \frac{1}{10}$ and $4 \div \frac{1}{10}$ .
What calculation did you do each time?
Use this pattern to find $18 \div \frac{1}{10}$ .
Explain how you could find $4 \div \frac{2}{10}$ and $4 \div \frac{8}{10}$ .

Problem 3

Find each quotient.

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

Problem 4

Use the fact that $2 \frac{1}{2} \div \frac{1}{8} = 20$ to find $2 \frac{1}{2} \div \frac{5}{8}$ . Explain or show your reasoning.

Problem 5 From Unit 4 Lesson 9

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.

Problem 6 From Unit 4 Lesson 7

A box contains $1 \frac{3}{4}$ pounds of pancake mix. Jada used $\frac{7}{8}$ pound for a recipe. What fraction of the pancake mix in the box did she use? Explain or show your reasoning. Draw a diagram, if needed.

Problem 7 From Unit 3 Lesson 14

Calculate each percentage mentally.

25% of 400
50% of 90
75% of 200
10% of 8,000
5% of 20