1. The document provides instructions and examples for dividing fractions. It explains that to divide by a fraction, you multiply by the reciprocal of the fraction. 2. Four examples are shown of dividing fractions step-by-step, simplifying the answers to simplest form. An example problem of cutting pieces from a board is also worked out. 3. The document explains how working with multiplying rational numbers helps with dividing fractions, since dividing by a fraction is the same as multiplying by the reciprocal.

1. Course 2, Lesson 4-8
Complete. Round to the nearest hundredth if necessary.
1. 16 in. ≈ cm
2. 35 g ≈ lb
3. 7 pt ≈ L
4. 15 km ≈ mi
5. Gina’s dog weighs 39 pounds. How many kilograms does it
weigh?
6. Thomas ran 3.5 miles. How many kilometers did he run?
7. A recipe calls for 4 cups of milk. How many milliliters of milk are
needed?

2. Course 2, Lesson 4-8
Answers
1. 40.64 2. 0.08
3. 3.31 4. 9.32
5. 17.69 6. 5.63
7. 946.36 mL

3. WHAT happens when you add,
subtract, multiply, and divide
fractions?
The Number System
Course 2, Lesson 4-8

4. Course 2, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.NS.2 Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
• 7.NS.2c Apply properties of operations as strategies to multiply and
divide rational numbers.
• 7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers.
• 7.EE.3 Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms
as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.

5. Course 2, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

6. • To divide fractions
• To divide mixed numbers
Course 2, Lesson 4-8
The Number System

7. Course 2, Lesson 4-8
The Number System
Words To divide by a fraction, multiply by its multiplicative inverse,
or reciprocal.
Examples Numbers Algebra
7 7
8 8
3 4
4 3
  , where , , 0
a c a d
b c d
b d b c
  

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Find ÷ 5.
Multiply by the reciprocal of , which is .
Multiply.
A whole number can be written as a fraction over 1.

9. Answer
Need Another Example?
Find ÷ 4. Write in simplest form.

10. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Find ÷ – . Write in simplest form.
Divide 4 and 2 by their GCF, 2.
Multiply.
Estimate 1 ÷ = –2
2
1
= – or –1
Check for Reasonableness – ≈ –2
Multiply by the reciprocal of – , which is – .

11. Answer
Need Another Example?
Find ÷ – . Write in simplest form.

12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Find ÷ 3 . Write in simplest form.
Multiply by the reciprocal of , which is .
Multiply.
Rename 3 a fraction greater than one.
Divide out common factors.
1
1 5
1

13. Answer
Need Another Example?
Find ÷ 2 . Write in simplest form.

14. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. The side pieces of a butterfly house are 8 inches
long. How many side pieces can be cut from a
board measuring 49 inches long?
Rename the mixed numbers as fractions
greater than one.
Multiply.
Use compatible numbers. 48 ÷ 8 = 6
Divide out common factors.
7
To find how many side pieces can be cut, divide 49 by 8 .
Estimate
Multiply by the reciprocal of , which is .
3
1 1
2
= or 6
So, 6 side pieces can be cut.
Check for Reasonableness Compare to the estimate. 6 = 6

15. Answer
Need Another Example?
A bottling machine needs to be restocked with new
lids every 2 hours. If the machine runs 19 hours,
how many times will it have to be restocked with
lids?
7 times

16. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-8
The Number System

17. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-8
The Number System
Sample answers:
• The multiplicative inverse of a fraction is its reciprocal.
• When you divide by a fraction, multiply by its
multiplicative inverse.

18. Course 2, Lesson 4-8
Ratios and Proportional RelationshipsThe Number System
Explain how your
work with multiplying
rational numbers
helped you with
this lesson.