1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Multiply. Write each answer in simplest form.
Warm Up
Multiply. Write each answer in simplest form.
• 2
• 3
• 3
• 1 1 2 __ 5 1 2 __ 1 2 __ 21 4 __ 1 4 _
or 5 1 3 __ 10 1 5 __ 1 4 __ 11 4 __ 3 4 __
or 2

3. Problem of the Day
Rachel is building a doghouse. She needs to cut a 12-foot-long board into lengths of 65 in. How many lengths can she cut, and will there be any wood left? If so, how much?
2 lengths; yes, 14 in.

4. Learn to divide fractions and mixed numbers.

5. Vocabulary
reciprocal
multiplicative inverse

6. Reciprocals can help you divide by fractions
Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1.

7. Additional Example 1A: Finding Reciprocals
Find the reciprocal. 1 9 __ 1 9 __ 1 9 __
• = 1
Think: of what number is 1? 1 9 __ 1 9 __
• 9 = 1 1 9 __ 9 1 __
of is 1. 1 9 __
The reciprocal of is 9.

8. Additional Example 1B: Finding Reciprocals
Find the reciprocal. 2 3 __ 2 3 __
• = 1 2 3 __
Think: of what number is 1? 2 3 __ 3 2 __ 6 __ 2 3 __ 3 2 __
• = = 1
of is 1. 2 3 __ 3 2 __
The reciprocal of is .

9. Additional Example 1C: Finding Reciprocals
Find the reciprocal. 1 5 __ 3 1 5 __ 16 5 __ 16 5 __
Write as .
• = 1 16 5 __ 5 16 __ 80 __ 16 5 __ 5 16 __
• = = 1
of is 1. 16 5 __ 5 16 __
The reciprocal of is

10. Check It Out: Example 1A Find the reciprocal. 1 4 __ 1 4 __ • = 1
• = 1
Think: of what number is 1? 1 4 __ 1 4 __
• 4 = 1 1 4 __ 4 1 __
of is 1. 1 4 __
The reciprocal of is 4.

11. Check It Out: Example 1B Find the reciprocal. 4 5 __ 4 5 __ • = 1 4 5
• = 1 4 5 __
Think: of what number is 1? 4 5 __ 5 4 __ 20 __ 4 5 __ 5 4 __
• = = 1
of is 1. 4 5 __ 5 4 __
The reciprocal of is .

12. Check It Out: Example 1C Find the reciprocal. 4 1 8 __ 1 8 __ 33 8 __
Write as .
• = 1 33 8 __ 8 33 __
___ 33 8 __ 8 33 __
• = = 1
of is 1. 33 8 __ 8 33 __
The reciprocal of is

13. Look at the relationship between the fractions and . If you switch the
numerator and denominator of a fraction,
you will find its reciprocal. Dividing by a
number is the same as multiplying by its
reciprocal. 3 4 __ 4 3 __ 1 4 __
24 ÷ 4 = 6
24 • = 6

14. Divide. Write each answer in simplest form.
Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers
Divide. Write each answer in simplest form. 8 7 __
÷ 7 8 7 __
Rewrite as multiplication using the
reciprocal of 7, 1 7 __ 8 7 __ 1 7 __
÷ 7 = •
8 • 1
7 • 7
____ =
Multiply by the reciprocal. 8 49 __ =
The answer is in simplest form.

15. When you divide by a proper fraction, the quotient will be greater than the dividend. For example, since there are 8 halves in 4, 4  ½ = 8.
Caution!

16. Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers5 6 __ 2 3 __ ÷
Rewrite as multiplication using the
reciprocal of , 5 6 __ 2 3 __ 5 6 __ 3 2 __
÷ = • 2 3 __ 3 2 __ 1
5 • 3
6 • 2
____ =
Simplify before multiplying. 2 5 4 __ =
Multiply. 1 4 __
You can write the answer as a mixed number.
= 1

17. Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers3 4 __ 1 12 __
2 ÷ 1
Write the mixed numbers as
improper fractions =
and = 3 4 __ 1 12 __ 11 4 __ 13 12 __ 3 4 __ 11 4 __
2 ÷ = ÷ 1 12 __ 13 12 __ 11 4 __ 12 13 __ =
Rewrite as multiplication. • 3
11 • 12
4 • 13
______ =
Simplify before multiplying. 1 33 13 __ =
Multiply. 7 13 __
You can write the answer as a mixed number.
= 2

18. Divide. Write each answer in simplest form.
Check It Out: Example 2A
Divide. Write each answer in simplest form. 2 3 __
÷ 3 2 3 __
Rewrite as multiplication using the
reciprocal of 3, . 1 3 __ 2 3 __ 1 3 __
÷ 3 = •
2 • 1
3 • 3
____ =
Multiply by the reciprocal. 2 9 __ =
The answer is in simplest form.

19. Check It Out: Example 2B ÷ 7 10 __ 1 5 __
Rewrite as multiplication using the
reciprocal of , 7 10 __ 1 5 __ 7 10 __ 5 1 __
÷ = • 1 5 __ 5 1 __ 1
7 • 5
10 • 1
____ =
Simplify before multiplying. 2 7 2 __ =
Multiply. 1 2 __
You can write the answer as a mixed number.
= 3

20. Check It Out: Example 2C 3 ÷ 1 2 3 __ 1 9 __
3 ÷ 1
Write the mixed numbers as
improper fractions =
and = 2 3 __ 1 9 __ 11 3 __ 10 9 __
÷ = ÷ 2 3 __ 11 3 __ 1 9 __ 10 9 __ 11 3 __ 9 10 __ =
Rewrite as multiplication. • 3
11 • 9
3 • 10
______ =
Simplify before multiplying. 1 33 10 __ =
Multiply. 3 10 __
You can write the answer as a mixed number.
= 3

21. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

22. Divide. Write each answer in simplest form. 3. ÷ 20 4. 3 ÷ 2
Lesson Quiz
Find the reciprocal.
Divide. Write each answer in simplest form.
÷ ÷ 2
5. Rhonda put 2 pounds of pecans into a -pound bag. How many bags did Rhonda fill? 1 11 __ 11 1 __ 8 13 __
13 8 __ 1 2 __ 1 2 __ 7 5 __ 2 5 __ 4 7 __ 1 35 __
, or 1 3 4 __ 1 4 __
11 bags

23. Lesson Quiz for Student Response Systems
1. Identify the reciprocal of
A. – C.
B D. 15

24. Lesson Quiz for Student Response Systems
2. Identify the reciprocal of
A C.
B D.

25. Lesson Quiz for Student Response Systems
3. Divide and identify the answer in the simplest form.
A C.
B D.

26. Lesson Quiz for Student Response Systems
4. Divide and identify the answer in the simplest form.
A C.
B D.

27. Lesson Quiz for Student Response Systems
5. In her pet care center, Nelson has pounds of cat food. He plans to feed a cat with pound of cat food. How many cats can he feed?
A. 13 cats C. 11 cats
B. 12 cats D. 10 cats