1. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Lesson 8: Dividing Fractions and Mixed Numbers
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
73
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Student Outcomes
 Students divide fractions by mixed numbers by first converting the mixed numbers into a fraction with a value
larger than one.
 Students use equations to find quotients.
Lesson Notes
There is some mandatory prep work before teaching the lesson. The memory game that is included in the lesson needs
to be cut and prepared for pairs or individual students.
Classwork
Example 1 (12 minutes): Introduction to Calculating the Quotient of a Mixed Number and a Fraction
 Carli has 4
1
2
walls left to paint in order for all the bedrooms in her house to have the same color paint.
However, she has used almost all of her paint and only has
5
6
of a gallon left. How much paint can she use on
each wall in order to have enough to paint the remaining walls?
 In order to solve the word problem, we must calculate the quotient of
5
6
÷ 4
1
2
.
Before dividing, discuss how the answer must be less than one because you are dividing a
smaller number by a larger number. Estimation could also be used to emphasize this
point: 1 ÷ 5 =
1
5
.
Explain that the mixed number must be converted into a fraction with a value larger than
one. You may also emphasize that converting mixed numbers to fractions with a value
larger than one is important for different division strategies. Have students complete this
conversion on their own and then share the process they followed.
Remind students about the formula they learned in the previous lesson and have them
attempt to solve the problem. Have students show the process used to find the quotient.
Scaffolding:
If students struggle with
converting mixed numbers into
fractions, a model may help.
On a number line, show
students how 9 steps of length
1
1
will end up at 4
.
2
2

2. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Example 1: Introduction to Calculating the Quotient of a Mixed Number and a Fraction
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
74
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
a. Carli has ퟒ ퟏ
ퟐ
walls left to paint in order for all the bedrooms in her house to have the same color paint. However,
she has used almost all of her paint and only has
ퟓ
ퟔ
of a gallon left. How much paint can she use on each wall in
order to have enough to paint the remaining walls?
Calculate the quotient:
ퟓ
ퟔ
÷ ퟒ
ퟏ
ퟐ
Convert into the fraction:
ퟗ
ퟐ
Divide fractions:
ퟓ
ퟔ
÷
ퟗ
ퟐ
=
ퟓ
ퟔ
×
ퟐ
ퟗ
=
ퟏퟎ
ퟓퟒ
=
ퟓ
ퟐퟕ
Carli can use
ퟓ
ퟐퟕ
of a gallon of paint on each of the remaining walls.
 Calculate the quotient.
2
5
÷ 3
4
7
Students solve this problem individually as the teacher walks around checking for understanding. Students then share
their answers and processes used to find the quotients. Provide time for students to ask questions.
b. Calculate the quotient.
ퟐ
ퟓ
÷ ퟑ
ퟒ
ퟕ
Convert into the fraction:
ퟐퟓ
ퟕ
Divide fractions:
ퟐ
ퟓ
÷
ퟐퟓ
ퟕ
=
ퟐ
ퟓ
×
ퟕ
ퟐퟓ
=
ퟏퟒ
ퟏퟐퟓ
Exercise 1 (25 minutes)
Students complete the memory game individually or in small groups.
The following are some important directions for the teacher to share with students:
 The goal is to match each expression with the equivalent quotient.
 Each expression is assigned a letter. Students must show their work in that box on the student materials. Once
they have solved a particular problem, they will not have to solve it again if they record their work in the correct
place.
 Students are able to flip two cards over during each turn. If the expression and the quotient do not match, both
cards should be flipped back over. If the expression and quotient do match, the student keeps the matches to
determine a winner at the end.
If students are not clear about the directions, the teacher may choose two or three problems for students to do as a
class to show how the memory game works.
MP.1

3. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
75
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
A.
3
4
÷ 6
2
3
9
80
B.
1
3
÷ 4
3
4
4
57
C.
2
5
÷ 1
7
8
16
75
D.
7
1
2
÷
5
6
9
E.
3
4
7
÷
5
8
5
5
7
F.
5
5
8
÷
9
10
6
1
4
G.
1
4
÷ 10
11
12
3
131
H.
5
3
4
÷
5
9
10
7
20
I.
3
1
5
÷
2
3
5
4
5
J.
3
5
÷ 3
1
7
21
110
K.
10
13
÷ 2
4
7
35
117
L.
2
1
4
÷
7
8
2
4
7

4. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
76
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exercise 1
Show your work for the memory game in the boxes provided below.
A.
ퟑ
ퟒ
÷ ퟔ
ퟐ
ퟑ
=
B.
ퟑ
ퟒ
÷
ퟐퟎ
ퟑ
=
C.
ퟑ
ퟒ
×
ퟑ
ퟐퟎ
=
ퟗ
ퟖퟎ
D.
ퟏ
ퟑ
÷ ퟒ
ퟑ
ퟒ
=
ퟏ
ퟑ
÷
ퟏퟗ
ퟒ
=
ퟏ
ퟑ
×
ퟒ
ퟏퟗ
=
ퟒ
ퟓퟕ
E.
ퟐ
ퟓ
÷ ퟏ
ퟕ
ퟖ
=
ퟐ
ퟓ
÷
ퟏퟓ
ퟖ
=
ퟐ
ퟓ
×
ퟖ
ퟏퟓ
=
ퟏퟔ
ퟕퟓ
F. ퟕ ퟏ
ퟐ
÷ ퟓ
ퟔ
= ퟏퟓ
ퟐ
÷ ퟓ
ퟔ
= ퟏퟓ
ퟐ
× ퟔ
ퟓ
= ퟗퟎ
ퟏퟎ
= ퟗ
G. ퟑ ퟒ
ퟕ
÷ ퟓ
ퟖ
= ퟐퟓ
ퟕ
÷ ퟓ
ퟖ
= ퟐퟓ
ퟕ
× ퟖ
ퟓ
= ퟐퟎퟎ
ퟑퟓ
= ퟓ ퟓ
ퟕ
H. ퟓ ퟓ
ퟖ
÷ ퟗ
ퟏퟎ
= ퟒퟓ
ퟖ
÷ ퟗ
ퟏퟎ
= ퟒퟓ
ퟖ
× ퟏퟎ
ퟗ
= ퟒퟓퟎ
ퟕퟐ
= ퟔ ퟏ
ퟒ
I.
ퟏ
ퟒ
÷ ퟏퟎ
ퟏퟏ
ퟏퟐ
=
ퟏ
ퟒ
÷
ퟏퟑퟏ
ퟏퟐ
=
ퟏ
ퟒ
×
ퟏퟐ
ퟏퟑퟏ
=
ퟏퟐ
ퟓퟐퟒ
=
ퟑ
ퟏퟑퟏ
J. ퟓ ퟑ
ퟒ
÷ ퟓ
ퟗ
= ퟐퟑ
ퟒ
÷ ퟓ
ퟗ
= ퟐퟑ
ퟒ
× ퟗ
ퟓ
= ퟐퟎퟕ
ퟐퟎ
= ퟏퟎ ퟕ
ퟐퟎ
K. ퟑ ퟏ
ퟓ
÷ ퟐ
ퟑ
= ퟏퟔ
ퟓ
÷ ퟐ
ퟑ
= ퟏퟔ
ퟓ
× ퟑ
ퟐ
= ퟒퟖ
ퟏퟎ
= ퟒ ퟒ
ퟓ
L.
ퟑ
ퟓ
÷ ퟑ
ퟏ
ퟕ
=
ퟑ
ퟓ
÷
ퟐퟐ
ퟕ
=
ퟑ
ퟓ
×
ퟕ
ퟐퟐ
=
ퟐퟏ
ퟏퟏퟎ
M.
ퟏퟎ
ퟏퟑ
÷ ퟐ
ퟒ
ퟕ
=
ퟏퟎ
ퟏퟑ
÷
ퟏퟖ
ퟕ
=
ퟏퟎ
ퟏퟑ
×
ퟕ
ퟏퟖ
=
ퟕퟎ
ퟐퟑퟒ
=
ퟑퟓ
ퟏퟏퟕ
N. ퟐ ퟏ
ퟒ
÷ ퟕ
ퟖ
= ퟗ
ퟒ
÷ ퟕ
ퟖ
= ퟗ
ퟒ
× ퟖ
ퟕ
= ퟕퟐ
ퟐퟖ
= ퟐ ퟒ
ퟕ
Closing (4 minutes)
 How does the process of dividing a fraction by a mixed number compare with our previous work with division of
fractions? Discuss similarities and differences.
Exit Ticket (4 minutes)

5. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Name ___________________________________________________ Date____________________
Lesson 8: Dividing Fractions and Mixed Numbers
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
77
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exit Ticket
Calculate the quotient.
1.
3
4
÷ 5
1
5
2.
3
7
÷ 2
1
2
3.
5
8
÷ 6
5
6
4.
5
8
÷ 8
3
10

6. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 6• 2
Lesson 8: Dividing Fractions and Mixed Numbers
Date: 12/5/14
78
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exit Ticket Sample Solutions
Calculate the quotient.
1.
ퟑ
ퟒ
÷ ퟓ
ퟏ
ퟓ
ퟑ
ퟒ
÷ ퟓ
ퟏ
ퟓ
=
ퟑ
ퟒ
÷
ퟐퟔ
ퟓ
=
ퟑ
ퟒ
×
ퟓ
ퟐퟔ
=
ퟏퟓ
ퟏퟎퟒ
2.
ퟑ
ퟕ
÷ ퟐ
ퟏ
ퟐ
ퟑ
ퟕ
÷ ퟐ
ퟏ
ퟐ
=
ퟑ
ퟕ
÷
ퟓ
ퟐ
=
ퟑ
ퟕ
×
ퟐ
ퟓ
=
ퟔ
ퟑퟓ
3.
ퟓ
ퟖ
÷ ퟔ
ퟓ
ퟔ
ퟓ
ퟖ
÷ ퟔ
ퟓ
ퟔ
=
ퟓ
ퟖ
÷
ퟒퟏ
ퟔ
=
ퟓ
ퟖ
×
ퟔ
ퟒퟏ
=
ퟑퟎ
ퟑퟐퟖ
=
ퟏퟓ
ퟏퟔퟒ
4.
ퟓ
ퟖ
÷ ퟖ
ퟑ
ퟏퟎ
ퟓ
ퟖ
÷ ퟖ
ퟑ
ퟏퟎ
=
ퟓ
ퟖ
÷
ퟖퟑ
ퟏퟎ
=
ퟓ
ퟖ
×
ퟏퟎ
ퟖퟑ
=
ퟓퟎ
ퟔퟔퟒ
=
ퟐퟓ
ퟑퟑퟐ
Problem Set Sample Solutions
Calculate each quotient.
1.
ퟐ
ퟓ
÷ ퟑ
ퟏ
ퟏퟎ
ퟐ
ퟓ
÷
ퟑퟏ
ퟏퟎ
=
ퟐ
ퟓ
×
ퟏퟎ
ퟑퟏ
=
ퟐퟎ
ퟏퟓퟓ
=
ퟒ
ퟑퟏ
2. ퟒ
ퟏ
ퟑ
÷
ퟒ
ퟕ
ퟏퟑ
ퟑ
÷
ퟒ
ퟕ
=
ퟏퟑ
ퟑ
×
ퟕ
ퟒ
=
ퟗퟏ
ퟏퟐ
= ퟕ
ퟕ
ퟏퟐ
3. ퟑ
ퟏ
ퟔ
÷
ퟗ
ퟏퟎ
ퟏퟗ
ퟔ
÷
ퟗ
ퟏퟎ
=
ퟏퟗ
ퟔ
×
ퟏퟎ
ퟗ
=
ퟏퟗퟎ
ퟓퟒ
= ퟑ
ퟐퟖ
ퟓퟒ
= ퟑ
ퟏퟒ
ퟐퟕ
4.
ퟓ
ퟖ
÷ ퟐ
ퟕ
ퟏퟐ
ퟓ
ퟖ
÷
ퟑퟏ
ퟏퟐ
=
ퟓ
ퟖ
×
ퟏퟐ
ퟑퟏ
=
ퟔퟎ
ퟐퟒퟖ
=
ퟏퟓ
ퟔퟐ