# Lesson 11

Using an Algorithm to Divide Fractions

### Problem 1

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

A:

Multiplying $$\frac{14}{15}$$ by 5 and then by $$\frac{1}{7}$$.

B:

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

C:

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

D:

Multiplying $$\frac{14}{15}$$ by 5 and then dividing by 7.

E:

Multiplying $$\frac{15}{14}$$ by 7 and then dividing by 5.

### Problem 2

Clare said that $$\frac{4}{3}\div\frac52$$ is $$\frac{10}{3}$$. She reasoned: $$\frac{4}{3} \boldcdot 5=\frac{20}{3}$$ 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

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

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

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

### Solution

(From Unit 4, Lesson 10.)

### Problem 6

Consider the problem: After charging for $$\frac13$$ of an hour, a phone is at $$\frac25$$ of its full power. How long will it take the phone to charge completely?

Decide whether each equation can represent the situation.

1. $$\frac13\boldcdot {?}=\frac25$$
2. $$\frac13\div \frac25={?}$$
3. $$\frac25 \div \frac13 ={?}$$
4. $$\frac25 \boldcdot {?}=\frac13$$

### Solution

(From Unit 4, Lesson 9.)

### Problem 7

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.