# Lesson 10

Dividing by Unit and Non-Unit Fractions

Let’s look for patterns when we divide by a fraction.

### 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, then 6 people can have apples. Here are some other calculations:

$$24 \div 4 = 6$$

$$24 \div 2 = 12$$

$$24 \div 1 = 24$$

$$24 \div \frac12 = {?}$$

1. Priya thinks the “?” represents a number less than 24. Do you agree? Explain or show your reasoning.

2. In the case of $$24 \div \frac12 = {?}$$, how many people can have apples?

### Problem 2

Here is a centimeter ruler.

1. Use the ruler to find $$1 \div \frac{1}{10}$$ and $$4 \div \frac{1}{10}$$.
2. What calculation did you do each time?

3. Use this pattern to find $$18 \div \frac{1}{10}$$.

4. Explain how you could find $$4\div \frac{2}{10}$$ and $$4\div \frac{8}{10}$$.

### Problem 3

Find each quotient.

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

### Problem 4

Use the fact that $$2\frac12 \div \frac18=20$$ to find $$2\frac12 \div \frac58$$. Explain or show your reasoning.

### Problem 5

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.

(From Unit 4, Lesson 9.)

### Problem 6

A box contains $$1\frac 34$$ pounds of pancake mix. Jada used $$\frac 78$$ 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.

(From Unit 4, Lesson 7.)

### Problem 7

Calculate each percentage mentally.

1. 25% of 400
2. 50% of 90
1. 75% of 200
2. 10% of 8,000
1. 5% of 20
(From Unit 3, Lesson 14.)