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BELL RINGER 10-111-4 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 DrivingExpression 1: 2($10.95) + 3($7.50) + 2($5.00) +
5(418.99) = $21.90 + $22.50 + $10 + $94.95
$149.35The 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 theproduct 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
Use the Distributive Property to rewrite 6 ● 54. Then evaluate.
6(60 – 6) = 360 – 36 = 324
You can use the distributive property to multiply numbers easier using mental math.
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
714So 14(51) = 71421. 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. See p. 27.Are 5x3 and 4x2 like terms?
25. 2(x + 4) 2x + 8
EXAMPLE 3Algebraic Expressions
A. Rewrite 12(y + 3) using the Distributive Property.Then simplify.12(y + 3) = 12 ● y + 12 ● 3 Distributive Property
= 12y + 36 Multiply.
Answer: 12y + 36
EXAMPLE 3Algebraic 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 Multiply.
Answer: 4y2 + 32y + 8
EXAMPLE 3
A. Simplify 6(x – 4).
EXAMPLE 3
B. Simplify 3(x3 + 2x2 – 5x + 7).
EXAMPLE 4Combine Like Terms
A. Simplify 17a + 21a.
17a + 21a = (17 + 21)a Distributive Property
= 38a Substitution
Answer: 38a
EXAMPLE 4Combine Like Terms
B. Simplify 12b2 – 8b2 + 6b.
12b2 – 8b2 + 6b = (12 – 8)b2 + 6b Distributive
Property
= 4b2 + 6bSubstitution
Answer: 4b2 + 6b
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 + 4m13m + 5p
37. 4(fg + 3g) + 5g 4fg + 12g + 5g
4fg + 17g
43. 3m + 5g + 6g + 11m11g + 14m
47. 2(6x + 4) + 7x2(6x) + 2(4) + 7x12x + 8 +7x
19x + 8
EXAMPLE 5Write 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 5Write 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 (+)
= 26x + 2y Substitution
Answer: 26x + 2y
EXAMPLE 5
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)
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.
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