1. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction
by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
36
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Student Outcomes
 Students use visual models such as fraction bars and area models to divide fractions by fractions with different
denominators.
 Students make connections between visual models and multiplication of fractions.
Classwork
Opening Exercise (2 minutes)
Begin class with a review of equivalent fractions. Ask each student for a new example of an equivalent fraction.
Students need to share how they know that the new fraction is equivalent to the old fraction.
Opening Exercise
Write at least three equivalent fractions for each fraction below. Be sure to show how the two fractions are related.
a.
ퟐ
ퟑ
Sample solutions include
ퟒ
ퟔ
,
ퟔ
ퟗ
,
ퟖ
ퟏퟐ
,
ퟏퟎ
ퟏퟓ
,
ퟏퟐ
ퟏퟖ
.
b.
ퟏퟎ
ퟏퟐ
Sample solutions include
ퟓ
ퟔ
,
ퟏퟓ
ퟏퟖ
,
ퟐퟎ
ퟐퟒ
,
ퟐퟓ
ퟑퟎ
,
ퟑퟎ
ퟑퟔ
.
Example 1 (3 minutes)
For the first example, students will be asked to solve a word problem using the skills they used in Lesson 3 to divide
fractions with the same denominator.
 Molly purchased 1
3
8
cups of strawberries. This can also be represented as
11
8
. She eats
2
8
cups in a serving.
How many servings did Molly purchase?
 This question is really asking me how many
2
8
are in
11
8
or, in other words, to divide eleven eighths by
two eighths. I can use a model to show that there are 5
1
2
servings in the
11
8
cups of strawberries.
MP.1

2. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
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Example 1
Molly purchased
ퟏퟏ
ퟖ
cups of strawberries. She eats
ퟐ
ퟖ
in a serving. How many servings did Molly purchase?
Use a model to prove your answer.
ퟎ
ퟏ
ퟖ
ퟐ
ퟖ
ퟑ
ퟖ
ퟒ
ퟖ
ퟓ
ퟖ
ퟔ
ퟖ
ퟕ
ퟖ
ퟖ
ퟖ
ퟗ
ퟖ
ퟏퟎ
ퟖ
ퟏퟏ
ퟖ
ퟏퟐ
ퟖ
Example 2 (3 minutes)
 Now imagine that Molly’s friend Xavier purchased
11
8
cups of strawberries and that he eats
3
4
cup servings. How
many servings has he purchased?
 He has purchased
11
6
servings or 1 and
5
6
servings. (This would be answered last after a brief
discussion using the questions that follow.)
 What is this question asking us to do?
 I am being asked to divide
11
8
cups into
3
4
cup servings.
 How does the problem differ from the first example?
 The denominators are different.
 What are some possible ways that we could divide these two fractions?
 I could change
3
4
to
6
8
. These fractions are equivalent. I scaled up from
3
4
by multiplying the top and
bottom by 2.
MP.1
ퟏ + ퟏ + ퟏ + ퟏ + ퟏ +
ퟏ
ퟐ
= ퟓ
ퟏ
ퟐ

3. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
38
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Example 2
Now imagine that Molly’s friend Xavier purchased
ퟏퟏ
ퟖ
cups of strawberries and that he eats
ퟑ
ퟒ
cup servings. How many
servings has he purchased? Use a model to prove your answer.
ퟎ
ퟏ
ퟖ
ퟐ
ퟖ
ퟑ
ퟖ
ퟒ
ퟖ
ퟓ
ퟖ
ퟔ
ퟖ
ퟕ
ퟖ
ퟖ
ퟖ
ퟗ
ퟖ
ퟏퟎ
ퟖ
ퟏퟏ
ퟖ
ퟏퟐ
ퟖ
There are 1 and
ퟓ
ퟔ
servings.
Example 3 (3 minutes)

3
4
÷
2
3
 What is this question asking us to do?

2
3
of what is
3
4
or how many
2
3
are in
3
4
.
Lead students through a brief discussion about this example:
 Is your answer larger or smaller than one? Why?
 Since
2
3
is less than
3
4
, we will have an answer that is larger than 1.
 Why is this question more difficult to model than the questions in Lesson 3?
 The fractions do not have common denominators.
 How can we rewrite this question to make it easier to model?
 We can create equivalent fractions with like denominators and then model and divide.
 We can also think of this as
9
12
÷
8
12
표r nine twelfths divided by eight twelfths. 9 units ÷ 8 units =
9
8
or 1
1
8
units.
ퟏ +
ퟓ
ퟔ
MP.1

4. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
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Example 3
Find the quotient:
ퟑ
ퟒ
÷
ퟐ
ퟑ
. Use a model to show your answer.
Exercises 1–5 (20 minutes)
Students will work in pairs or alone to solve more questions about division of fractions with unlike denominators.
Exercises 1–5
A model should be included in your solution.
1.
ퟔ
ퟐ
÷
ퟑ
ퟒ
We could rewrite this problem to ask
ퟏퟐ
ퟒ
÷
ퟑ
ퟒ
=
ퟏퟐ
ퟑ
= ퟒ.
ퟏ + ퟏ + ퟏ + ퟏ
ퟎ
ퟏ
ퟏퟐ
ퟐ
ퟏퟐ
ퟑ
ퟏퟐ
ퟒ
ퟏퟐ
ퟓ
ퟏퟐ
ퟔ
ퟏퟐ
ퟕ
ퟏퟐ
ퟖ
ퟏퟐ
ퟗ
ퟏퟐ
ퟏퟎ
ퟏퟐ
ퟏퟏ
ퟏퟐ
0
ퟏ
ퟒ
ퟐ
ퟒ
ퟑ
ퟒ
ퟒ
ퟒ
ퟓ
ퟒ
ퟔ
ퟒ
ퟕ
ퟒ
ퟖ
ퟒ
ퟗ
ퟒ
ퟏퟎ
ퟒ
ퟏퟏ
ퟒ
ퟏퟐ
ퟒ
ퟖ
ퟖ
ퟏ
ퟖ
MP.1

5. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
ퟏ +
.
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
40
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
2.
ퟐ
ퟑ
÷
ퟐ
ퟓ
We could rewrite this problem to ask
ퟏퟎ
ퟏퟓ
÷
ퟔ
ퟏퟓ
=
ퟏퟎ
ퟔ
or ퟏ ퟒ
ퟔ
.
ퟎ
ퟏ
ퟏퟓ
ퟐ
ퟏퟓ
ퟑ
ퟏퟓ
ퟒ
ퟏퟓ
ퟓ
ퟏퟓ
ퟔ
ퟏퟓ
ퟕ
ퟏퟓ
ퟖ
ퟏퟓ
ퟗ
ퟏퟓ
ퟏퟎ
ퟏퟓ
ퟏퟏ
ퟏퟓ
3.
ퟕ
ퟖ
÷
ퟏ
ퟐ
We could rewrite this as
ퟕ
ퟖ
÷
ퟒ
ퟖ
=
ퟕ
ퟒ
or ퟏ ퟑ
ퟒ
ퟒ
ퟖ
ퟖ
ퟖ
ퟏ +
ퟑ
ퟒ
4.
ퟑ
ퟓ
÷
ퟏ
ퟒ
This can be rewritten as
ퟏퟐ
ퟐퟎ
÷
ퟓ
ퟐퟎ
=
ퟏퟐ
ퟓ
= ퟐ
ퟐ
ퟓ
.
ퟏ + ퟏ +
ퟐ
ퟓ
ퟒ
ퟔ

6. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
.
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
41
ퟎ
ퟏ
ퟏퟐ
ퟐ
ퟏퟐ
ퟑ
ퟏퟐ
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
5.
ퟓ
ퟒ
÷
ퟏ
ퟑ
We can rewrite this as
ퟏퟓ
ퟏퟐ
÷
ퟒ
ퟏퟐ
= fifteen twelfths ÷ four twelfths = ퟏퟓ
ퟒ
= ퟑ ퟑ
ퟒ
Closing (10 minutes)
 When dividing fractions, is it possible to get a whole number quotient?
 When dividing fractions, is it possible to get an answer that is larger than the dividend?
 When you are asked to divide two fractions with different denominators, what is one possible way to solve?
Exit Ticket (5 minutes)
ퟒ
ퟏퟐ
ퟓ
ퟏퟐ
ퟔ
ퟏퟐ
ퟕ
ퟏퟐ
ퟖ
ퟏퟐ
ퟗ
ퟏퟐ
ퟏퟎ
ퟏퟐ
ퟏퟏ
ퟏퟐ
ퟏ
ퟏퟑ
ퟏퟐ
ퟏퟒ
ퟏퟐ
ퟏퟓ
ퟏퟐ
ퟏퟔ
ퟏퟐ
ퟏퟕ
ퟏퟐ

7. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Name ___________________________________________________ Date____________________
Lesson 4: Interpreting and Computing Division of a Fraction by a
Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
42
© 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
Draw a model to support your answer to the division questions.
1.
9
4
÷
3
8
2.
3
5
÷
2
3

8. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
43
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exit Ticket Sample Solutions
Draw a model to support your answer to the division questions.
1.
ퟗ
ퟒ
÷
ퟑ
ퟖ
This can be rewritten as
ퟏퟖ
ퟖ
÷
ퟑ
ퟖ
= eighteen eighths divided by three eighths =
ퟏퟖ
ퟑ
= ퟔ.
2.
ퟑ
ퟓ
÷
ퟐ
ퟑ
This can be rewritten as
ퟗ
ퟏퟓ
÷
ퟏퟎ
ퟏퟓ
= nine fifteenths divided by ten fifteenths or ퟗ units ÷ ퟏퟎ units.
So this is equal to
ퟗ
ퟏퟎ
.
0
ퟏ
ퟏퟓ
ퟐ
ퟏퟓ
ퟑ
ퟏퟓ
ퟒ
ퟏퟓ
ퟓ
ퟏퟓ
ퟔ
ퟏퟓ
ퟕ
ퟏퟓ
ퟖ
ퟏퟓ
ퟗ
ퟏퟓ
ퟏퟎ
ퟏퟓ
ퟏퟏ
ퟏퟓ
ퟗ units
ퟏퟎ units

9. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Problem Set Sample Solutions
The following problems can be used as extra practice or a homework assignment.
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
1.
ퟖ
ퟗ
÷
ퟒ
ퟗ
Eight ninths ÷ four ninths = ퟐ.
ퟎ
ퟏ
ퟗ
ퟐ
ퟗ
ퟑ
ퟗ
ퟒ
ퟗ
ퟓ
ퟗ
ퟔ
ퟗ
ퟕ
ퟗ
ퟖ
ퟗ
ퟗ
ퟗ
ퟏퟎ
ퟗ
ퟏퟏ
ퟗ
2.
ퟗ
ퟏퟎ
÷
ퟒ
ퟏퟎ
Nine tenths ÷ four tenths = ퟐ
ퟏ
ퟒ
.
ퟏ ퟏ
ퟏ
ퟒ
3.
ퟑ
ퟓ
÷
ퟏ
ퟑ
ퟗ
ퟏퟓ
÷
ퟓ
ퟏퟓ
= nine fifteenths ÷ five fifteenths =
ퟗ
ퟓ
= ퟏ
ퟒ
ퟓ
.
ퟎ
ퟏ
ퟏퟓ
ퟐ
ퟏퟓ
ퟑ
ퟏퟓ
ퟒ
ퟏퟓ
ퟓ
ퟏퟓ
ퟔ
ퟏퟓ
ퟕ
ퟏퟓ
ퟖ
ퟏퟓ
ퟗ
ퟏퟓ
ퟏퟎ
ퟏퟓ
ퟏퟏ
ퟏퟓ
ퟏ +
ퟒ
ퟓ

10. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 4 6• 2
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—
More Models
Date: 12/1/14
45
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
4.
ퟑ
ퟒ
÷
ퟏ
ퟓ
ퟏퟓ
ퟐퟎ
÷
ퟒ
ퟐퟎ
= fifteen twentieths ÷ four twentieths =
ퟏퟓ
ퟒ
.
ퟏ + ퟏ + ퟏ +
ퟑ
ퟒ
= ퟑ
ퟑ
ퟒ
ퟒ
ퟒ
+
ퟒ
ퟒ
+
ퟒ
ퟒ
+
ퟑ
ퟒ
=
ퟏퟓ
ퟒ