The Distributive
Property
Objectives To recognize the general patterns used to write the
distributive
property; and to mentally compute products using
d
distributive strategies.
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ePresentations
eToolkit
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Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Apply equivalent names for sums
and differences. [Number and Numeration Goal 4]
• Recognize patterns in number sentences
of partial products. [Patterns, Functions, and Algebra Goal 1]
• Write special cases for basic arithmetic
operations. [Patterns, Functions, and Algebra Goal 1]
• Recognize order of operations in using
and applying distributive strategies. [Patterns, Functions, and Algebra Goal 3]
• Use distributive strategies to mentally
compute products. [Patterns, Functions, and Algebra Goal 4]
Family
Letters
Students apply the distributive property to
simplify algebraic expressions and mentally
calculate products. They also use the
distributive property to factor expressions.
Ongoing Learning & Practice
1 2
4 3
Playing Getting to One
Student Reference Book, p. 321
Math Masters, p. 448
per partnership: calculator; overhead
calculator (optional)
Students practice comparing decimal
numbers and apply proportional
reasoning skills.
Math Boxes 9 2
Math Journal 2, p. 329
straightedge
Students practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 3. Study Link 9 2
Math Masters, p. 286
Students practice and maintain skills
through Study Link activities.
Ongoing Assessment:
Informing Instruction See page 795.
Key Vocabulary
distributive property
Materials
Math Journal 2, pp. 328–328B
Student Reference Book, pp. 248 and 249
Study Link 91
slate
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 289–291
Unit 9
Common
Core State
Standards
[Number and Numeration Goal 2]
Key Activities
792
Assessment
Management
More about Variables, Formulas, and Graphs
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
ENRICHMENT
Writing Number Stories
Math Journal 2, p. 328
Students write number stories that can
be solved using the distributive property.
EXTRA PRACTICE
Applying the Distributive Property
Math Masters, p. 287
Students use the distributive property
to solve problems.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 130
Students add the term distributive property
to their Math Word Banks.
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, SMP8
Getting Started
Content Standards
6.NS.4, 6.EE.2, 6.EE.2b, 6.EE.3
Mental Math and Reflexes
Math Message
Be ready to explain how to mentally find the
following products:
Students find the total number of objects in a set when
a fractional part of the set is given. Suggestions:
4 ∗ 36 = ?
1
_
of the people in the room is 6. 36
99 ∗ 8 = ?
$11.50 ∗ 5 = ?
6
1
_
of the books on a shelf is 12. 108
9
Study Link 9 1 Follow-Up
5
Briefly review the answers.
2
_
of the marbles in a bag is 18. 45
7
_
of the crayons in a box is 56. 64
8
4
_
of the pages in a book is 40. 150
15
6
_
of the questions on a test is 108. 126
7
Discuss students’ strategies. Some students may prefer solving
the problems by first translating them to equations. For example,
4
4
_
_
15 of the pages in a book is 40 can be translated as 15 ∗ x = 40.
1 Teaching the Lesson
▶ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
ELL
Students share solution strategies. Help them record their
strategies as number sentences. Be sure to include distributive
strategies as you record solutions.
Examples:
4 ∗ 36 = 4 ∗ (30 + 6)
= (4 ∗ 30) + (4 ∗ 6) = 120 + 24 = 144, or
4 ∗ 36 = 4 ∗ (40 - 4)
= (4 ∗ 40) - (4 ∗ 4) = 160 - 16 = 144
99 ∗ 8 = (100 - 1) ∗ 8
= (100 ∗ 8) - (1 ∗ 8) = 800 - 8 = 792, or
99 ∗ 8 = (90 + 9) ∗ 8
= (90 ∗ 8) + (9 ∗ 8) = 720 + 72 = 792
$11.50 ∗ 5 = ($12.00 - $0.50) ∗ 5
= ($12.00 ∗ 5) - ($0.50 ∗ 5)
= $60.00 - $2.50 = $57.50, or
$11.50 ∗ 5 = ($11.00 + $0.50) ∗ 5
= ($11.00 ∗ 5) + ($0.50 ∗ 5)
= $55.00 + $2.50 = $57.50
Lesson 9 2
793
Student Page
Algebra
Adjusting the Activity
The Distributive Property
You have been using the distributive property for years,
probably without knowing it.
For example, when you solve 40 * 57 with partial products, you
think of 57 as 50 7 and multiply each part by 40.
The distributive property says: 40 * (50 7) (40 * 50) (40 * 7).
The distributive property can be illustrated by finding the area
of a rectangle.
57
* 40
40 * 50 2000
40 * 7 280
40 * 57 2280
Show how the distributive property works by finding
the area of the rectangle in two different ways.
To extend the activity and review order of operations, write the
expressions without parentheses.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Ask students to look for patterns in the number sentences.
Include the following points in your discussion:
Method 1 Find the total width of the rectangle and multiply
that by the height.
A 3 cm * (4 cm 2 cm)
3 cm * 6 cm
18 cm2
One of the factors is rewritten as a sum (or difference) of
two numbers, each of which can be easily multiplied by the
other factor.
Method 2 Find the area of each smaller rectangle, and then add these areas.
A (3 cm * 4 cm) (3 cm * 2 cm)
12 cm2 6 cm2
18 cm2
Both methods show that the area of the rectangle is 18 cm2.
3 * (4 2) (3 * 4) (3 * 2).
This is an example of the distributive property of multiplication over addition.
The distributive property of multiplication over addition can be
stated in two ways:
a * (x y) (a * x) (a * y)
Parentheses are useful for keeping track of this sum (or
difference) when it is rewritten.
The original product becomes the sum (or difference) of two
simple products.
(x y) * a (x * a) (y * a)
This strategy for making mental calculations is based on the
distributive property. This property gets its name because the
factor outside the parentheses is distributed to each of the terms
within the parentheses. To support English language learners,
model the meaning of the word distribute. (See margin.)
Student Reference Book, p. 248
▶ Summarizing the
The papers are distributed to each student.
WHOLE-CLASS
DISCUSSION
Distributive Property
(Student Reference Book, pp. 248 and 249)
The factor is distributed to each term.
Student Page
Algebra
The distributive property of multiplication over subtraction can
also be stated in two ways:
Algebraic Thinking Use the two examples on pages 248 and 249 of
the Student Reference Book to discuss how the distributive property
summarizes students’ work in Lesson 9-1. Then review the four
different general patterns for the distributive property. Remind
students that, as with other equations, they can interchange the
left and right sides.
Distributive Property of Multiplication over Addition
a ∗ (x + y) = (a ∗ x) + (a ∗ y)
a * (x y) (a * x) (a * y)
(x y) * a (x * a) (y * a)
(x + y) ∗ a = (x ∗ a) + (y ∗ a)
Show how the distributive property of multiplication
over subtraction works by finding the area of the
shaded part of the rectangle in two different ways.
Method 1 Multiply the width of the shaded rectangle
Distributive Property of Multiplication over Subtraction
by its height.
a ∗ (x - y) = (a ∗ x) - (a ∗ y)
A 3 cm * (6 cm 2 cm)
3 cm * 4 cm
12 cm2
(x - y) ∗ a = (x ∗ a) - (y ∗ a)
Method 2 Subtract the area of the unshaded rectangle
from the entire area of the whole rectangle.
A (3 cm * 6 cm) (3 cm * 2 cm)
18 cm2 6 cm2
12 cm2
Both methods show that the area of the shaded part of the rectangle is 12 cm2.
3 * (6 2) (3 * 6) (3 * 2)
This is an example of the distributive property of multiplication over subtraction.
Use the distributive property to solve the problems.
1. 6 * (100 40)
2. (35 15) * 6
3. 4 * (80 7)
4. Use a calculator to verify that 1.23 * (456 789) (1.23 * 456) (1.23 * 789).
Check your answers on page 423.
Student Reference Book, p. 249
794
Unit 9
More about Variables, Formulas, and Graphs
Student Page
Make sure students understand that these general statements
do not show four different properties but are different ways of
stating the same general property. Demonstrate this by writing
special cases.
Date
Time
LESSON
9 2
248 249
The distributive property is a number property that combines multiplication with addition or
multiplication with subtraction. The distributive property can be stated in 4 different ways.
Multiplication over Addition
Examples:
a ∗ (x + y) = (a ∗ x) + (a ∗ y)
7 ∗ (30 + 5) = (7 ∗ 30) + (7 ∗ 5) = 245
The Distributive Property
Multiplication over Subtraction
For any numbers a, x, and y:
For any numbers a, x, and y:
a º (x y) (a º x ) (a º y)
y)
(x y ) º a (x º a) (y º a)
a º (x y) (a º x) (a º y)
(x y) º a (x º a) (y º a)
Use the distributive property to fill in the blanks.
1.
(x + y) ∗ a = (x ∗ a) + (y ∗ a)
(30 + 5) ∗ 7 = (30 ∗ 7) + (5 ∗ 7) = 245
a ∗ (x - y) = (a ∗ x) - (a ∗ y)
7 ∗ (40 - 5) = (7 ∗ 40) - (7 ∗ 5) = 245
6 º 34 (
3.
(6 º 70) (6 º 4) 4.
(
5.
8 º (90 3) (
6.
(50 º 7) (8 º
7.
9 º (20 7) (9 º
9.
10.
11.
12.
13.
14.
15.
16.
Ongoing Assessment: Informing Instruction
6
2.
8.
(x - y) ∗ a = (x ∗ a) - (y ∗ a)
(40 - 5) ∗ 7 = (40 ∗ 7) - (5 ∗ 7) = 245
4 º (70 8) (4 º
40
6
70
) (4 º
º 30) (
6
6
8
º (70 4
) º 8 (40 º 8) (6 º
8
7
)
º 4)
)
8
)
º 90) (8 º 3)
) ( 50 8 ) º 7
20 ) ( 9 º 7)
4 º (5 6) ( 4 º 5 ) ( 4 º 6 )
(41 19) º 7 ( 41 º 7 ) ( 19 º 7 )
r ) ( 4 º r)
(18 4) º r (18 º
7 º (w 6 ) ( 7 º w) ( 7 º 6)
n º (13 27) ( n º 13 ) ( n º 27 )
(f 8) º 15 ( f
º 15 ) ( 8 º 15 )
(29 º x) (12 º x) ( 29 12 ) º x
(6 º d) (6 º 7)
6 º (d 7) (5 º 12) (5 º h)
5 º (12 h) Math Journal 2, p. 328
Students may recognize that they can use the Commutative Property of
Multiplication to write the second general pattern and special case in each
example. Although they can also change the order of numbers or expressions
being added, watch for students who try to change the order in which numbers
or expressions are subtracted.
Pose problems that students can solve mentally by applying the
distributive property. Suggestions:
6 ∗ 57 342
99 ∗ 80 7,920
14 ∗ 10.5 147
1 ∗ 42 63
1_
2
103 ∗ 31 3,193
998 ∗ 201 200,598
▶ Using the Distributive Property
PARTNER
ACTIVITY
(Math Journal 2, p. 328)
Game Master
Name
Date
Time
Getting to One Record Sheets
Algebraic Thinking The problems on journal page 328 provide
practice with four different ways of stating the distributive
property. For most of the problems, there are many ways to fill
in the blanks to obtain true sentences. Each problem, however,
has a unique solution in the form of the distributive property. For
example, in Problem 1, 4 ∗ (70 + 8) = (4 ∗ 50) + (4 ∗ 28) is a true
sentence, but 4 ∗ (70 + 8) = (4 ∗ 70) + (4 ∗ 8) is the only solution
in the form of the distributive property. When students have
finished, go over their answers.
1 2
4 3
321
Player’s Name ______________________ Player’s Name ______________________
Draw a line to separate each round.
Guess
Display
on calculator
(to nearest 0.01)
Result
Write:
L if too large
S if too small
✔ if exact
Draw a line to separate each round.
Guess
Display
on calculator
(to nearest 0.01)
Result
Write:
L if too large
S if too small
✔ if exact
Adjusting the Activity
Divide journal page 328 into two sections—problems without variables
(Problems 1–9) and problems with variables (Problems 10–16). Have students
use a blank sheet of paper to cover the second section while they work on the
first section.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Math Masters, p. 448
Lesson 9 2
795
▶ Factoring with the
WHOLE-CLASS
ACTIVITY
Distributive Property
(Math Journal 2, pp. 328–328B)
Have students look at Problem 5 on journal page 328. Remind
them that this problem illustrates how the distributive property
can be used to mentally solve the multiplication problem 8 ∗ 93.
Tell students that when they apply the distributive property to
solve multiplication problems mentally, they are distributing a
number across a sum. In Problem 5, the 8 is distributed across
the sum 90 + 3. This process is called expanding the expression
8 ∗ (90 + 3).
Now have students look at Problem 6. Ask them how Problem 6 is
different from Problem 5. Sample answer: The left side of the
equation in Problem 6 shows the expression expanded. Tell
students that in this problem, the 7 is “undistributed” from the
expression (50 ∗ 7) + (8 ∗ 7). Applying the distributive property
in this way is called factoring the expression (50 ∗ 7) + (8 ∗ 7).
Because 7 is a factor of both 50 ∗ 7 and 8 ∗ 7, it is a factor of the
whole expression.
In all the examples of factored expressions students have seen so
far, the two addends have been written as products. Tell students
that they can use their knowledge of greatest common factors
to factor an expression even if the two addends are written as
whole numbers.
Write 33 + 12 on the board. Walk students through the
following steps to help them use the distributive property to
factor this expression:
Step 1: Find the greatest common factor of 33 and 12.
List the factors of 33: 1, 3, 11, and 33.
List the factors of 12: 1, 2, 3, 4, 6, and 12.
From the lists, you can see that the greatest common factor of
33 and 12 is 3.
Step 2: Write 33 and 12 as products, with their GCF as one of
the factors.
33 = 3 ∗ 11
12 = 3 ∗ 4
Step 3: Rewrite the original sum, substituting the products from
Step 2 for the addends.
33 + 12 = 3 ∗ 11 + 3 ∗ 4
Step 4: Use the distributive property to factor the expression on
the right side of the equal sign, or “undistribute” the 3.
33 + 12 = 3 ∗ (11 + 4)
795A Unit 9
More about Variables, Formulas, and Graphs
Student Page
Point out that because you factored out the greatest common
factor, the addends 11 and 4 have no common factor other than 1.
Help students use mathematical language to express the meaning
of the final number sentence. You might use language such as
the following:
●
3 is a factor of the expression 33 + 12.
●
The sum 33 + 12 is a multiple of the sum 11 + 4.
●
Factoring 3 out of the expression 33 + 12 produces the
expression 3 ∗ (11 + 4).
Date
Time
LESSON
92
Factoring Sums
The Distributive Property of Multiplication over Addition
a ∗ (x + y ) = a ∗ x + a ∗ y
(a ∗ x ) + (a ∗ y ) = a ∗ (x + y )
(x + y ) ∗ a = x ∗ a + y ∗ a
(x ∗ a) + (y ∗ a) = (x + y ) ∗ a
The equation 21 + 15 = 3 ∗ (7 + 5) is a special case of the distributive property in
which the addends on the left side are written as whole numbers instead of products.
This equation tells you a lot about these numbers. Here are some true statements
about the relationships among the numbers and expressions in this equation:
3 is a factor of both 21 and 15.
3 is a factor of the expression 21 + 15.
Write other sums on the board. Ask students to identify the
greatest common factor of the addends and use the GCF to factor
the expression. Encourage students to check that the final two
addends have no common factor other than 1. Suggestions:
18 + 26 2; 2 ∗ (9 + 13)
24 + 36 12; 12 ∗ (2 + 3)
The expression 21 + 15 is a multiple of the expression 7 + 5.
When you use the distributive property to write 21 + 15 as 3 ∗ (7 + 5), we say you
factor 3 out of the sum 21 + 15.
You can use the distributive property to factor a sum of any two whole numbers. In
this activity, you will factor out the greatest common factor of two addends. You will
be rewriting the original sum as a multiple of another sum whose addends have no
common factors other than 1.
Complete the following steps for each sum.
a.
Find the greatest common factor of the two addends.
b.
Use the distributive property to factor the GCF out of the sum. Complete the
number sentence to show the result.
c.
Fill in the blanks to give an example of what your number sentence shows.
Example: 16 + 6
2
a.
Greatest common factor:
b.
Number sentence: 16 + 6 =
c.
Fill in the blanks: The expression
the expression
2
8 +3
8 + 3 )
∗(
16 + 6 is a multiple of
.
25 + 20 5; (5 + 4) ∗ 5
Math Journal 2, p. 328A
27 + 15 3; 3 ∗ (9 + 5)
328A_328B_EMCS_S_G6_MJ2_U09_576442.indd 328A
3/9/11 11:13 AM
21 + 35 7; 7 ∗ (3 + 5)
44 + 52 4; (11 + 13) ∗ 4
When students seem comfortable with the procedure, read journal
page 328A as a class. Then have students work with a partner to
complete the problems on journal page 328B.
Student Page
Date
Time
LESSON
Factoring Sums
92
continued
Follow the directions on journal page 328A.
1.
2.
3.
4.
5.
18 + 10
2
a.
Greatest common factor:
b.
Number sentence: 18 + 10 =
c.
Fill in the blanks:
2
2
9
∗(
is a factor of the sum
+
5
18
+
)
10
.
30 + 25
5
a.
Greatest common factor:
b.
Number sentence: 30 + 25 = (
c.
Fill in the blank: The expression 30 + 25 is a
expression 6 + 5.
6
5 )∗ 5
multiple of the
+
48 + 28
a.
Greatest common factor:
b.
Number sentence:
c.
Fill in the blanks:
and 28.
48
4
27 + 63
4
+
28
∗(
12
+
7 )
48
9
a.
Greatest common factor:
b.
Number sentence:
c.
Fill in the blanks: When the number
27 + 63
4
=
is the greatest common factor of the numbers
Sample answer: 27 + 63 = 9 ∗ (3 + 7)
9
is factored out of the sum
, the result is the expression 9 ∗ (3 + 7).
36 + 60
a.
Greatest common factor:
b.
Number sentence:
c.
Write your own sentence.
12
Sample answer: 36 + 60 = 12 ∗ (3 + 5)
Sample answer: The sum 36 + 60 is a
multiple of the sum 3 + 5.
Math Journal 2, p. 328B
328A_328B_EMCS_S_G6_MJ2_U09_576442.indd 328B
3/9/11 11:13 AM
Lesson 9 2 795B
Student Page
Games
Links to the Future
Getting to One
Materials 1 calculator
Players
2
Skill
Estimation
Students will apply their knowledge of the distributive property when they factor
and multiply polynomials in future algebra courses.
Object of the game To correctly guess a mystery number in
as few tries as possible.
Directions
1. Player 1 chooses a mystery number that is between
1 and 100.
For a decimal number, the
places to the right of the
decimal point with digits
in them are called decimal
places. For example, 4.06
has 2 decimal places,
123.4 has 1 decimal place,
and 0.780 has 3
decimal places.
2. Player 2 guesses the mystery number.
3. Player 1 uses a calculator to divide Player 2’s guess by the
mystery number. Player 1 then reads the answer in the
calculator display. If the answer has more than 2 decimal
places, only the first 2 decimal places are read.
4. Player 2 continues to guess until the calculator result is 1.
Player 2 keeps track of the number of guesses.
5. When Player 2 has guessed the mystery number, players
trade roles and follow Steps 1–4 again. The player who
guesses their mystery number in the fewest number of
guesses wins the round. The first player to win 3 rounds
wins the game.
▶ Playing Getting to One
Player 1 chooses the mystery number 65.
Player 2 guesses: 45. Player 1 keys in: 45
Answer: 0.69 Too small.
65
.
Player 2 guesses: 73. Player 1 keys in: 73
Answer: 1.12 Too big.
65
.
Player 2 guesses: 65. Player A keys in: 65
Answer: 1. Just right!
65
.
2 Ongoing Learning & Practice
PARTNER
ACTIVITY
(Student Reference Book, p. 321; Math Masters, p. 448)
Divide the class into pairs. Distribute a calculator and a game
record sheet (Math Masters, p. 448) to each partnership. Students
read the directions on page 321 in their Student Reference Book. If
an overhead calculator is available, ask a volunteer to demonstrate
how to play the game. Encourage students to play a practice game.
Advanced Version
Allow mystery numbers up to 1,000.
Student Reference Book, p. 321
▶ Math Boxes 9 2
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 329)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-4. The skill in Problem 5
previews Unit 10 content.
Writing/Reasoning Have students write a response to the
following: Explain how you found the coordinates of the
⎯⎯⎯ in Problem 5d. Sample answer: For the x
midpoint of AB
value of the midpoint, I found the mean of the x-coordinates. For
the y value of the midpoint, I found the mean of the y-coordinates.
Student Page
Date
Time
LESSON
1.
Use the distributive property to fill in
the blanks.
a.
b.
c.
d.
2.
Circle the expressions that represent the
area of the rectangle.
m
8 º (30 4) 8
9
(
º 30 ) ( 8 º 4 )
(
º 7) ( 9 º 6) 9 º (7 6)
(20 6) º 10 (20 º 10) (6 º 10 )
5 (9 12) (5)(9) (5)(12)
Find the number.
1
a. 10
4.
of what number is 17?
3
b. 4
of what number is 75?
2
c. 5
of what number is 14?
3
d. 20
7
e. 8
of what number is 9?
of what number is 84?
170
100
35
60
96
2
a.
4m 8
b.
4 º 2m
c.
8m
d.
(m 2) º 4
e.
4(2 m)
f.
8 2m
Write , , or .
a.
36 (2)
23 º 78
400 º 3 20
2 15 / 3 7 º 10
3
2
12
7
6 7
3
2
9
28 (15)
1
b. 2
c.
d.
e.
3
4
()
▶ Study Link 9 2
2
1
(Math Masters, p. 286)
y
Home Connection Students practice using the
distributive property.
5
4
Plot (4,2). Label it A.
b.
Plot (4,2). Label it B.
c.
Draw line segment AB.
d.
Name the coordinates
—
of the midpoint of AB.
(
0
,
0
)
B
3
2
1
0
1
2
3
4
5
x
A
234
Math Journal 2, p. 329
796
Unit 9
INDEPENDENT
ACTIVITY
9
Plot and label points on the coordinate
grid as directed.
a.
[Number and Numeration Goal 2]
248 249
81 82
5.
Math Boxes
Problem 3
Use Math Boxes, Problem 3 to assess students’ ability to find the total number
of objects in a set when a fractional part of the set is given. Students are making
adequate progress if they complete parts a–e. Some students might be able to
mentally solve these problems.
4
248 249
3.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
9 2
More about Variables, Formulas, and Graphs
Study Link Master
Name
3 Differentiation Options
ENRICHMENT
▶ Writing Number Stories
Date
STUDY LINK
Time
Using the Distributive Property
92
Reminder: a º (x y) (a º x) (a º y)
a º (x y) (a º x) (a º y)
1.
INDEPENDENT
ACTIVITY
15–30 Min
(Math Journal 2, p. 328)
To further explore applications of the distributive property,
students choose expressions on journal page 328 and make up
number stories that fit those expressions.
2.
Example: 4 ∗ (70 + 8)
Four friends shared a pile of coins. Each person received 7 dimes
and 8 pennies. How much money was originally in the pile?
3.
Have students share their stories with other students.
248 249
Use the distributive property to rewrite each expression.
7
7
7
a.
7 (3 4) (
b.
7 (3 π) (
c.
7 (3 y) (
d.
7 (3 (2 4)) (
e.
7 (3 (2 π)) (
f.
7 (3 (2 y)) (
º
º
º
3
3
3
7
7
7
7
7
7
)(
)(
)(
3
3
3
)(
)(
)(
4
y
7
7
7
)
)
)
(2 4))
(2 (
2
))
y
))
Use the distributive property to solve each problem. Study the first one.
(7 110) + (7 25) 770 + 175 945
a.
7 (110 25) b.
20 (42 19) (20 42) (20 19) 840 380 460
c.
(32 50) 40 (32 40) (50 40) 1,280 2,000 3,280
d.
(90 8) 11 (90 11) (8 11) 990 88 902
e.
9 (15 25) (9 15) (9 25) 135 225 360
Circle the statements that are examples of the distributive property.
a.
(80 5) (120 5) (80 120) 5 b. 6 (3 0.5) (6 3) 0.5
c.
12(d t) 12d 12t
d.
(a c) n a n c n
e.
(16 4m) 9.7 16 (4m 9.7)
f.
(9 º ) ( º ) (9 ) º 1
2
1
3
1
2
1
3
1
2
Practice
Write each quotient in lowest terms.
EXTRA PRACTICE
▶ Applying the
INDEPENDENT
ACTIVITY
1
4. 5
3
1
15
3
5. 7
11
14
6
11
6.
1
19
1
2
1 7
8
57
Math Masters, p. 286
5–15 Min
Distributive Property
(Math Masters, p. 287)
To provide extra practice applying the distributive property,
have students write number models to show how they solved
number stories.
ELL SUPPORT
▶ Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 130)
Teaching Master
To provide language support for vocabulary terms, have students
use the Word Bank template found on Differentiation Handbook,
page 130. Ask students to write distributive property and represent
the term with a picture and other words that describe it. See the
Differentiation Handbook for more information.
Name
LESSON
92
1.
Date
Time
Applying the Distributive Property
Cheng and 5 of his friends are buying lunch.
Each person gets a hamburger and a soda.
How much money will they spend in all?
Write a number model to show
how you solved the problem.
Answer
$.90
Sample answer:
$1.10
6 (1.10 0.90) c
$12.00
Explain how the distributive property can help you solve Problem 1.
Sample answer: Using the distributive
property, you can first add the two values 1.10
and 0.90 and then multiply the sum by 6.
2.
Minowa signed her new book at a local bookstore. In the morning she
signed 36 books, and in the afternoon she signed 51 books. It took her
5 minutes to sign each. How much time did she spend signing books?
Write a number model to show
how you solved the problem.
7 hours and 15 minutes
Answer
3.
Ms. Hays bought fabric for the school musical chorus. She bought 4 yards
each of one kind for 30 group costumes and 4 yards each of another kind
for 6 soloists. How many yards did she buy in all? Sample answer:
Write a number model to show
how you solved the problem.
(30 4) (6 4) y
144 yards
Answer
4.
Sample answer:
(36 51) 5 t
Mr. Katz gave a party because all the students got 100% on their math test. He had
budgeted $1.15 per student. It turned out that he saved $0.25 per student. If there
are 30 students, how much did he spend? Sample answer:
Write a number model to show
how you solved the problem.
Answer
(30 1.15) (30 0.25) n
$27.00
Fill in the missing numbers according to the distributive property.
5.
28 6 (
20
8
)6
6.
(
20
6) (
8
6) (20 8) 6
Math Masters, p. 287
Lesson 9 2
797