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5-6 Dividing Fractions and Mixed Numbers
Warm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
5-6 Dividing Fractions and Mixed Numbers
Warm UpMultiply. Write each answer in simplest form.
1. 2 • 2
2. 1 • 3
3. 3 • 3
4. 2 • 1
5
or 5
10
15__
12__
12__
12__
13__
14__
214__
or 2114__ 3
4__
14_
5-6 Dividing Fractions and Mixed Numbers
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.
5-6 Dividing Fractions and Mixed Numbers
Learn to divide fractions and mixed numbers.
5-6 Dividing Fractions and Mixed Numbers
Vocabulary
reciprocal
multiplicative inverse
5-6 Dividing Fractions and Mixed Numbers
Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1.
5-6 Dividing Fractions and Mixed Numbers
Additional Example 1A: Finding Reciprocals
Find the reciprocal.
19__
19__ • = 1 Think: of what number is 1?
19__1
9__
19__ • 9 = 1 of is 1.
19__ 9
1__
The reciprocal of is 9.19__
5-6 Dividing Fractions and Mixed Numbers
Additional Example 1B: Finding Reciprocals
Find the reciprocal.
23__
23__ • = 1 Think: of what number is 1?
23__
32__2
3__ • = = 1
66__ of is 1.
23__ 3
2__
The reciprocal of is .23__ 3
2__
5-6 Dividing Fractions and Mixed Numbers
15__
165__ • = 1 Write 3 as . 1
5__
516__16
5__ • = = 1
8080__ of is 1.
165__ 5
16__
The reciprocal of is .165__ 5
16__
165__
Additional Example 1C: Finding Reciprocals
Find the reciprocal.
3
5-6 Dividing Fractions and Mixed Numbers
Check It Out: Example 1A
Find the reciprocal.
14__
14__ • = 1 Think: of what number is 1?
14__
14__ • 4 = 1 of is 1.
14__ 4
1__
The reciprocal of is 4.14__
5-6 Dividing Fractions and Mixed Numbers
Check It Out: Example 1B
Find the reciprocal.
45__
45__ • = 1 Think: of what number is 1?
45__
54__4
5__ • = = 1
2020__ of is 1.
45__ 5
4__
The reciprocal of is .45__ 5
4__
5-6 Dividing Fractions and Mixed Numbers
18__
338__ • = 1 Write 4 as . 1
8__
833__33
8__ • = = 1
264 264___ of is 1.
338__ 8
33__
The reciprocal of is .338__ 8
33__
338
__
Check It Out: Example 1C
Find the reciprocal.
4
5-6 Dividing Fractions and Mixed Numbers
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.
34__ 4
3__
24 ÷ 4 = 6 24 • = 614__
5-6 Dividing Fractions and Mixed Numbers
Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
÷ 7 87__
87__ ÷ 7 = •
Rewrite as multiplication using the
reciprocal of 7, . 17__
Multiply by the reciprocal.
87
__ 17__
8 • 17 • 7____ =
The answer is in simplest form.
=
849__
5-6 Dividing Fractions and Mixed Numbers
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!
5-6 Dividing Fractions and Mixed Numbers
Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers
÷ 56__
56__ ÷ = •
Rewrite as multiplication using the
reciprocal of , . 32__
Simplify before multiplying.
56
__ 32__
5 • 36 • 2____ =
You can write the answer as a mixed number.
=
54__
23__
23__ 2
3__
1
2
Multiply.
= 1
14__
5-6 Dividing Fractions and Mixed Numbers
Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers
2 ÷ 1 34__
Write the mixed numbers as
improper fractions. 2 =
and 1 = 1312__
Rewrite as multiplication.
11 • 12
4 • 13______
=
You can write the answer as a mixed number.
=
3313__
112__
34__
1
3Simplify before multiplying.
= 2
713__
2 ÷ 1 = ÷3
4__ 1
12__ 11
4__ 13
12__ 11
4__
112__
11
4__ 12
13__ •
Multiply. =
5-6 Dividing Fractions and Mixed Numbers
Check It Out: Example 2A
Divide. Write each answer in simplest form.
÷ 3 23__
23__ ÷ 3 = •
Rewrite as multiplication using the
reciprocal of 3, . 13__
Multiply by the reciprocal.
23
__ 13__
2 • 13 • 3____ =
The answer is in simplest form.
=
29__
5-6 Dividing Fractions and Mixed Numbers
Check It Out: Example 2B
÷ 710__
710__ ÷ = •
Rewrite as multiplication using the
reciprocal of , . 51__
Simplify before multiplying.
710__ 5
1__
7 • 510 • 1____ =
You can write the answer as a mixed number.
=
72__
15__
15__ 1
5__
1
2
Multiply.
= 3 12__
5-6 Dividing Fractions and Mixed Numbers
Check It Out: Example 2C
3 ÷ 1 23__
Write the mixed numbers as
improper fractions. 3 =
and 1 = . 109__
Rewrite as multiplication.
11 • 9
3 • 10______
=
You can write the answer as a mixed number.
=
3310__
19__
23__
1
3Simplify before multiplying.
= 3
310__
3 ÷ 1 = ÷2
3__ 1
9__ 11
3__ 10
9__ 11
3__
19__
11
3__ 9
10__ •
Multiply. =
5-6 Dividing Fractions and Mixed Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz
Find the reciprocal.
1. 2.
Divide. Write each answer in simplest form.
3. ÷ 20 4. 3 ÷ 2
5. Rhonda put 2 pounds of pecans into a -pound
bag. How many bags did Rhonda fill?
111__ 8
13__
47__ 1
2__ 1
2__
34__ 1
4__
111__ 13
8__
135__ 7
5 __ 2
5__, or 1
11 bags
5-6 Dividing Fractions and Mixed Numbers
1. Identify the reciprocal of .
A. –15 C.
B. D. 15
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
2. Identify the reciprocal of .
A. 15 C.
B. 7 D.
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
3. Divide and identify the answer in the simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
4. Divide and identify the answer in the simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
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
Lesson Quiz for Student Response Systems
