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5-6 Dividing Fractions and Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-6 Dividing Fractions and Mixed Numbers
Warm Up
Multiply. Write each answer in simplest
form.
1
1. 2 __
2
1
2. 1 __
2
•
2
5
•
1
3 __
21
_
__ or 5 1
4
4
2
1
3. 3 __
•3
3
4.
1
__
25 •
1
__
14
10
11
3
__ or 2 __
4
4
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
5-6 Dividing Fractions and Mixed Numbers
Reciprocal: 2 numbers whose
product = 1
Reciprocals help you divide fractions.
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
1
__
9
1
1
__
__
•
= 1 Think: 9 of what number is 1?
9
1
9
1
__
__
__
of
is 1.
• 9 =1
9
1
9
1
__
The reciprocal of 9 is 9.
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
2
__
3
2
__
•
=1
3
3
2 __
6
__
__
•
=
=1
3 2
6
2
__
Think: 3 of what number is 1?
2
3
__
of __ is 1.
3
2
3
2
__
__
The reciprocal of 3 is 2 .
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
1
__
3 5
16
__ •
=1
5
5
16
80
__ • __
= __ = 1
5 16
80
1
16
Write 3 __ as __ .
5
5
16
5
__ of __
is 1.
5
16
5
16
The reciprocal of __ is __ .
16
5
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
1
__
4
1
__
•
=1
4
1
__
• 4 =1
4
1
__
Think: 4 of what number is 1?
1
4
__
of __ is 1.
4
1
1
__
The reciprocal of 4 is 4.
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
4
__
5
4
__
•
=1
5
5
4 __
20
__
•
= __ = 1
5 4
20
4
__
Think: 5 of what number is 1?
4
5
__
of __ is 1.
5
4
5
4
__
__
The reciprocal of 5 is 4 .
5-6 Dividing Fractions and Mixed Numbers
Find the reciprocal.
1
__
4
8
33
__ •
=1
8
8
33
264
__ • __
= ___ = 1
8 33
264
1
__.
Write 4 __ as 33
8
8
33
8
__ of __
is 1.
8
33
33
8
__
__
The reciprocal of 8 is 33 .
5-6 Dividing Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
8
__
÷7
7
8
8
1
__
÷ 7 = __ • __
7
7
7
Rewrite as multiplication using the
1
__
reciprocal of 7,
.
7
• 1
____
= 8
7•7
Multiply by the reciprocal.
8
= __
49
The answer is in simplest form.
5-6 Dividing Fractions and Mixed Numbers
Caution!
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.
5-6 Dividing Fractions and Mixed Numbers
2
5
__
÷ __
3
6
2
5 __
5
3
__
÷
= __ • __
3
6
6
2
1
• 3
____
= 5
6•2
2
5
= __
4
1
__
=1
4
Rewrite as multiplication using the
3
2
__
__
reciprocal of 3 , 2 .
Simplify before multiplying.
Multiply.
You can write the answer as a
mixed number.
5-6 Dividing Fractions and Mixed Numbers
Change ALL Mixed numbers to Improper
fractions FIRST then divide
1
3
2 __
÷ 1 __
4
12
3
1
11 13
2 __ ÷ 1 __ = __ ÷ __
4
12
4
12
11
= __
4
12
• __
13
3
11
• 12
______
=
4 • 13
1
33
= __
13
7
__
=2
13
Write the mixed numbers as
3
11
improper fractions. 2 __ = __
4
4
1
13
__
__
and 1
=
12
12
Rewrite as multiplication.
Simplify before multiplying.
Multiply.
You can write the answer as a
mixed number.
5-6 Dividing Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
2
__
÷3
3
2
2
1
__
÷ 3 = __ • __
3
3
3
• 1
____
= 2
3•3
2
= __
9
Rewrite as multiplication using the
1
__
reciprocal of 3,
.
3
Multiply by the reciprocal.
The answer is in simplest form.
5-6 Dividing Fractions and Mixed Numbers
1
7
__
÷ __
5
10
1
7
7
5
__
÷ __ = __ • __
5
10
10 1
1
• 5
____
= 7
10 • 1
2
7
= __
2
1
= 3 __
2
Rewrite as multiplication using the
5
1 __
__
reciprocal of 5 , 1 .
Simplify before multiplying.
Multiply.
You can write the answer as a
mixed number.
5-6 Dividing Fractions and Mixed Numbers
1
2
3 __
÷ 1 __
3
9
Write the mixed numbers as
1
2
11
10
__
__
__
__
3
÷1
=
÷
2
11
__
__
9
3
3
9 improper fractions. 3
=
10
1
__
__
and 1 9 = 9 .
11
= __
3
9
• __
10
3
3
Rewrite as multiplication.
11 • 9 3
______
=
Simplify before multiplying.
3 • 10
1
33
= __
10
3
__
=3
10
Multiply.
You can write the answer as a
mixed number.
5-6 Dividing Fractions and Mixed Numbers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz
Find the reciprocal.
1
11
__
1. __
2.
11
1
Divide. Write each answer
4 ÷ 20
3. __
7
1
__
35
8
__
13
13
__
8
in simplest form.
2
1 __
7 , or 1 __
1
__
__
4. 3 2 ÷ 2 2
5
5
3
1 -pound
__
5. Rhonda put 2 pounds of pecans into a __
4
4
bag. How many bags did Rhonda fill?
11 bags
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz for Student Response Systems
1. Identify the reciprocal of
.
A. –15
C.
B.
D. 15
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz for Student Response Systems
2. Identify the reciprocal of
A. 15
C.
B. 7
D.
.
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz for Student Response Systems
3. Divide and identify the answer in the
simplest form.
A.
C.
B.
D.
5-6 Dividing Fractions and Mixed Numbers
Lesson Quiz for Student Response Systems
4. Divide and identify the answer in the
simplest form.
A.
C.
B.
D.
5-6 Dividing Fractions and Mixed Numbers
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