# Lesson 7

Finding an Algorithm for Dividing Fractions

### 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

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

### Problem 3

Divide $$4\frac12$$ by each of these unit fractions.

1. $$\frac18$$
2. $$\frac14$$
3. $$\frac16$$

### Problem 4

Consider the problem: Kiran has $$2\frac34$$ pounds of flour. When he divides the flour into equal-sized bags, he fills $$4\frac18$$ bags. How many pounds fit in each bag?

Write a multiplication equation and a division equation to represent the question. Then, find the answer and show your reasoning.

### Problem 5

Elena and Noah are each filling a bucket with water. Noah’s bucket is $$\frac25$$ full and the water weighs $$2\frac12$$ pounds. How much does Elena’s water weigh if her bucket is full and her bucket is identical to Noah’s?

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

### Solution

(From Unit 3, Lesson 5.)

### Problem 6

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