# Illustrative Mathematics Unit 6.4, Lesson 11: Using an Algorithm to Divide Fractions

Learning Targets:

• I can describe and apply a rule to divide numbers by any fraction.

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Illustrative Math

### Lesson 11: Using an Algorithm to Divide Fractions

Let’s divide fractions using the rule we learned.

Illustrative Math Unit 6.4, Lesson 11 (printable worksheets)

### Lesson 11 Summary

The following diagram shows how to divide numbers by any fraction using an algorithm. ### Lesson 11.1 Multiplying Fractions

Evaluate each expression.

1. ⅔ · 27
2. ½ · ⅔
3. 2/9 · 3/5
4. 27/100 · 200/9
5. (1¾) · 5/7

Scroll down the page for the answer to the “Are you ready for more?” section.

### Lesson 11.2 Dividing a Fraction by a Fraction

Work with a partner. One person should work on the questions labeled “Partner A,” and the other should work on those labeled “Partner B.”

1. Partner A.
Find the value of each expression, and answer the question by completing the diagram that has been started for you. Show your reasoning.
• Show Diagram Show Applet

2. Partner B.
Elena said: “If you want to divide 4 by ⅖, you can multiply 4 by 5, then divide it by 2 or multiply it by ½.”
Find the value of each expression using the strategy that Elena described.
a. ¾ ÷ ⅛
b. 9/10 ÷ 3/5
Pause here for a discussion with your partner.
3. Complete this statement based on your observations:
To divide a number n by a fraction a/b, we can multiply n by ________ and then divide the product by ________.
4. Select all equations that represent the statement you completed.
a. n ÷ a/b = n · b ÷ a
b. n ÷ a/b = n · a ÷ b
c. n ÷ a/b = n · a/b
d. n ÷ a/b = n · b/a

#### Lesson 11.3 Using an Algorithm to Divide Fractions

1. Calculate each quotient using your preferred strategy. Show your work and be prepared to explain your strategy.
a. 8/9 ÷ 4
b. ¾ ÷ ½
c. 3⅓ ÷ 2/9
d. 9/2 ÷ 3/8
e. 6⅔ ÷ 3
2. After biking 5½ miles, Jada has traveled ⅔ of the length of her trip. How long (in miles) is the entire length of her trip? Write an equation to represent the situation, and find the answer using your preferred strategy.

#### Are you ready for more?

You have a pint of grape juice and a pint of milk. Transfer 1 tablespoon from the grape juice into the milk and mix it up. Then transfer 1 tablespoon of the mixture back to the grape juice. Which mixture is more contaminated?

The milk mixture is more contaminated because the first tablespoon transfered to the milk consists of grape juice whereas the second tablespoon transfered to the grape juice consists of milk and a bit of grape juice.

#### Lesson 11 Practice Problems

1. Select all statements that show correct reasoning for finding 14/15 ÷ 7/5.
A. Multiplying 14/15 by 5 and then by 1/7.
B. Dividing 14/15 by 5, and then multiplying by 1/7.
C. Multiplying 14/15 by 7, and then multiplying by 1/5.
D. Multiplying 14/15 by 5 and then dividing by 7.
2. Clare said that 4/3 ÷ 5/2 is 10/3. She reasoned: 4/3 · 5 = 20/3 and 20/3 · 2 = 10/3.
Explain why Clare’s answer and reasoning are incorrect. Find the correct quotient.
3. Find the value of 15/4 ÷ 5/8. Show your reasoning.
4. Kiran has 2¾ pounds of flour. When he divides the flour into equal-sized bags, he fills 4⅛ bags. How many pounds fit in each bag?
Write a multiplication equation and a division equation to represent the question and then answer the question. Show your reasoning.
5. Divide 4½ by the following unit fractions.
a. ⅛
b. ¼
c. ⅙
6. After charging for ⅓ of an hour, a phone is at ⅔ of its full power. How long will it take the phone to charge completely?
Decide whether each equation can represent the situation.
a. ⅓ · ? = ⅖
b. ⅓ ÷ ⅖ = ?
c. ⅖ ÷ ⅓ = ?
d. ⅖ · ? = ⅓
7. Elena and Noah are each filling a bucket with water. Noah’s bucket is ⅖ full and the water weighs 2½ pounds. How much does Elena’s bucket weigh if her bucket is full and her bucket is identical to Noah’s?
a. Write multiplication and division equations to represent the question.
b. Draw a diagram to show the relationship between the quantities and to answer the question.

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