Transcript 1-4 The Distributive Property 4A 10-12

BELL RINGER 10-11
1-4 READING QUIZ
1. What is the Title of Lesson 1-4?
 2. What is the Distributive Property?
 3. What are 2 ways that the Distributive
property can be used?
 4. What is a term?
 5. When is an expression written in simplest
form?

Keep your Homework - Review/Questions
REVIEW QUESTIONS IN NOTEBOOK 10-11
1. What is the difference between the
multiplicative inverse and additive inverse?
2. Does the commutative property always,
sometimes or never hold for subtraction?
Explain your reasoning.
3. What is the difference between the
commutative and reflexive property?
4. What is the school’s focus the next few
weeks?
P. 20 #29
29. Scuba Driving
Expression 1:
2($10.95) + 3($7.50) + 2($5.00) + 5(418.99) =
$21.90 + $22.50 + $10 + $94.95
$149.35
The total sales are $149.35.
Expression 2:
2($10.95 + $5) + 3($7.50) + 5($18.99)
2($15.95) + $22.50 + $94.95
$31.90 + $22.50 + $94.95
$149.35

#51
 51. Geometry: A regular octagon measures (3x
+ 5) units on each side. What is the perimeter if
x = 2?
Each side is 3x + 5 units.
3(2) + 5 = 11
So each side of the octagon is 11 units.
How do you find the perimeter of a shape?
Add all the sides.
How many sides does an octagon have?
(11)(8) = 88
So the perimeter is 88 units.
CCSS
Content Standards
A.SSE.1a Interpret parts of an expression,
such as terms, factors, and coefficients.
A.SSE.2 Use the structure of an
expression to identify ways to rewrite it.
Mathematical Practices
1 Make sense of problems and persevere
in solving them.
8 Look for and express regularity in
repeated reasoning.
THEN/NOW
You explored Associative and
Commutative Properties.
• Use the Distributive Property to
evaluate expressions.
• Use the Distributive Property to
simplify expressions.
VOCABULARY
• like terms
• simplest form
• coefficient
LESSON 1-4 DISTRIBUTIVE PROPERTY
Objectives:
By the end of class, students will be able to:

 Use
the distributive property to evaluate and
simplify expressions.
with 90% or above mastery.
CONCEPT
EXAMPLE 1
Distribute Over Addition
FITNESS Julio walks 5 days a week. He walks at
a fast rate for 7 minutes and cools down for 2
minutes. Use the Distributive Property to write
and evaluate an expression that determines the
total number of minutes Julio walks.
Understand You need to find the total number of
minutes Julio walks in a week.
Plan
Julio walks 5 days for 7 + 2 minutes
a day.
Solve
Write an expression that shows the
product of the number of days that
Julio walks and the sum of the
number of minutes he walks at each
rate.
EXAMPLE 1
Distribute Over Addition
5(7 + 2) = 5(7) + 5(2)
Distributive Property
= 35 + 10
Multiply.
= 45
Add.
Answer: Julio walks 45 minutes a week.
Check: The total number of days he walks is 5
days, and he walks 9 minutes per day.
Multiply 5 by 9 to get 45. Therefore, he
walks 45 minutes per week.
EXAMPLE 1
WALKING Susanne walks to school and home
from school 5 days each week. She walks to
school in 15 minutes and then walks home in 10
minutes. Rewrite 5(15 + 10) using the
Distributive Property. Then evaluate to find the
total number of minutes Susanne spends walking
to and home from school.
EXAMPLE 2
You can use the distributive property to multiply numbers easier
using mental math.
Use the Distributive Property to rewrite 6 ● 54.
Then evaluate.
6(60 – 6) =
360 – 36 =
324
DISTRIBUTIVE PROPERTY AND
MULTIPLYING NUMBERS
Next example
7(49) =
7(50 – 1)
7(50) + 7(-1)
350 – 7 = 343
Do p. 29 #2 and 21
DISTRIBUTIVE PROPERTY AND
MULTIPLYING NUMBERS
2. 14(51) =
14(50 + 1)
14(50) + 14(1)
700 + 14
714
So 14(51) = 714
21. 7  497
7(500 – 3)
7(500) – 7(3)
3500 – 21 =
3,479
DISTRIBUTIVE PROPERTY AND
SIMPLIFYING EXPRESSIONS
You can also use the distributive property to
simplify expressions.
 When is an expression in simplest form?
 An expression is in simplest form when it has
no like terms or parentheses.
 A term is a number, variable or a product of a
number and a variable.
 What are like terms?
 Like terms have the same variable and power.

EXAMPLE 3 Algebraic Expressions
A. Rewrite 12(y + 3) using the Distributive
Property.
Then simplify.
12(y + 3) =
12 ● y + 12 ● 3
Distributive Property
= 12y + 36
Answer: 12y + 36
Multiply.
EXAMPLE 3 Algebraic Expressions
B. Rewrite 4(y2 + 8y + 2) using the Distributive
Property. Then simplify.
4(y2 + 8y + 2) = 4(y2) + 4(8y) + 4(2) Distributive
Property
= 4y2 + 32y + 8
Answer: 4y2 + 32y + 8
Multiply.
EXAMPLE 3
A. Simplify 6(x – 4).
EXAMPLE 3
B. Simplify 3(x3 + 2x2 – 5x + 7).
EXAMPLE 4 Combine Like Terms
A. Simplify 17a + 21a.
17a + 21a = (17 + 21)a
= 38a
Answer: 38a
Distributive Property
Substitution
EXAMPLE 4 Combine Like Terms
B. Simplify 12b2 – 8b2 + 6b.
12b2 – 8b2 + 6b = (12 – 8)b2 + 6b Distributive
Property
= 4b2 + 6b
Answer: 4b2 + 6b
Substitution
Example:
C. -3(3m + 5m)
-3(3m) - 3(5m)
-9m - 15m like terms
-24m
EXAMPLE 4
D. Simplify 6n2 + 7n + 8n.
Do p. 29 27, 31 – 37odd, 43 and 47 in your
notebook
27. (4 – 3m)8
4(8) – 3m(8)
32 – 24m
31. 7m + 7 – 5m
2m + 7
33. (2 – 4n)17
2(17) – 4n (17)
34 – 68n
35. 7m + 2m + 5p + 4m
13m + 5p
37. 4(fg + 3g) + 5g
4fg + 12g + 5g
4fg + 17g
43. 3m + 5g + 6g + 11m
11g + 14m
47. 2(6x + 4) + 7x
2(6x) + 2(4) + 7x
12x + 8 +7x
19x + 8
EXAMPLE 5 Write and Simplify Expressions
Use the expression six times the sum of x and y
increased by four times the difference of 5x and
y.
A. Write an algebraic expression for the verbal
expression.
Answer: 6(x + y) + 4(5x – y)
EXAMPLE 5 Write and Simplify Expressions
B. Simplify the expression and indicate the
properties used.
6(x + y) + 4(5x – y)
= 6(x) + 6(y) + 4(5x) – 4(y)
Distributive
Property
= 6x + 6y + 20x – 4y
Multiply.
= 6x + 20x + 6y – 4y
Commutative (+)
=
Substitution
26x +
2y
Answer: 26x + 2y
EXAMPLE 5
Use the expression three times the difference of
2x and y increased by two times the sum of 4x
and y.
A. Write an algebraic expression for the verbal
expression.
A. 3(2x + y) + 2(4x – y)
B. 3(2x – y) + 2(4x + y)
C. 2(2x – y) + 3(4x + y)
D. 3(x – 2y) + 2(4x + y)
EXAMPLE 5
B. Simplify the expression 3(2x – y) + 2(4x + y).
CONCEPT
Additional Examples:
-(4x – 6)
-1(4x – 6)
-1(4x) – 1(-6)
-4x + 6
2 ( 15x + 45y + 75) + 8y
3
10x + 30 y + 25 + 8y =
10x + 38y + 25
4(x + 3) – (5x + 10)
4(x) + 4(3) – 1(5x) – 1(10)
4x + 12 – 5x – 10
-x + 2
HOMEWORK 10--11
p. 29-30 14, 18, 22, 26 – 36 even, 42 – 46
even, 50, 52, 57
Read 1-5 Take Notes
EXIT SLIP 10-11
1. What is the distributive property?
 2. What are like terms?
 3. Use the distributive property to simplify
3(2x + 6).
4. Simplify 6(x – 9) + 15x
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