Transcript Properties - Skyline R2 School

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Objective
Use addition and multiplication
properties to solve problems
Vocabulary
Equivalent expressions
Expressions that have the same value
4+3=7
5+2=7
6+1=7
Vocabulary
Properties
Statements that are true for any number or
variable
Distributive Property
Property
Distributive
Algebra
Arithmetic
a(b + c) = ab + ac
4(6 + 2) = 4(6) + 4(2)
a(b - c) = ab - ac
3(7 - 5) = 3(7) - 3(5)
3 (4 + 6) = 3(4) + 3(6)
Properties
Property
Commutative
Associative
Identity
Algebra
Arithmetic
a+b=b+a
6+1=1+6
a·b=b·a
7·3=3·7
a + (b + c) = (a + b) + c
2 + (3 + 8) = (2 + 3) + 8
a · (b · c) = (a · b) · c
3 · (4 · 5) = (3 · 4) · 5
a+0=a
9+0=9
a·1=a
5·1=5
Example 1 Use the Distributive Property
Example 2 Use the Distributive Property
Example 3 Use the Distributive Property
Example 4 Identify Properties
Example 5 Identify Properties
Example 6 Identify Properties
Example 7 Identify Properties
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Write the expression
8(5 + 7)
Distribute the factor 8 to the
numbers inside the parentheses
8(5) + 8(7)
Distribute the 8 to the 5
Bring down the +
Distribute the 8 to the 7
1/7
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Follow the order of operations
P
E
MD AS
8(5) + 8(7)
Multiply first
40 + 56
Multiply 8(5)
96
Bring down
+
Multiply 8(7)
Add 40 + 56
Answer: 96
1/7
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Answer: 36
1/7
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Write the expression
(2 + 9)6
Distribute the factor 6 to the
numbers inside the parentheses
(2)6 + (9)6
Distribute the 6 to the 2
Bring down the +
Distribute the 6 to the 9
2/7
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Follow the order of operations
(2)6 + (9)6
P
E
MD AS
Multiply first
12 + 54
66
Multiply (2)6
Bring down
+
Multiply (9)6
Add 12 + 54
Answer: 66
2/7
Use the Distributive Property to write
as an equivalent expression. Then evaluate the
expression.
Answer: 56
2/7
VACATIONS Mr. Harmon has budgeted $150 per day
for his hotel and meals during his vacation. If he
plans to spend six days on vacation, how much will
he spend?
6 (150)
Decide how to solve the problem
Spend $150 per day
6 days
Remember: per refers to multiplication
Write expression
3/7
VACATIONS Mr. Harmon has budgeted $150 per day for
his hotel and meals during his vacation. If he plans to
spend six days on vacation, how much will he spend?
6 (150)
6 (100 + 50)
6(100) + 6(50)
Use the distributive property to solve
Decompose 150
Distribute the factor 6 to the numbers
inside the parentheses
Distribute the 6 to the 100
Bring down the +
Distribute the 6 to the 50
3/7
Follow the order of operations
P
E
MD AS
6(100) + 6(50)
Multiply first
Multiply 6(100)
600 + 300
900
Bring down
+
Multiply 6(50)
Add 600 + 300
Label answer
Answer:
$900 spent on trip
3/7
COOKIES Heidi sold cookies for $2.50 per box for a
fundraiser. If she sold 60 boxes of cookies, how much
money did she raise?
Answer: $150
3/7
Name the property shown by the statement
7 = 1  7

Write problem
Determine property
Identity Property
Of Multiplication
Multiplying by 1 keeps the same
identity of the number
The process is multiplying
Answer: Identity Property of Multiplication
4/7
Name the property shown by the statement
Answer: Identity Property of Multiplication
4/7

.
Name the property shown by the statement
24 + 5 = 5 + 24
Write problem
Determine property
Commutative Property
Of Addition
The numbers have been switched
with each other but everything else
remains the same
Refers to the Commutative Property
The process is adding
Answer: Commutative Property of Addition
5/7
Name the property shown by the statement
Answer: Commutative Property of Addition
5/7
Name the property shown by the statement
7 + 0 = 7
Write problem
Determine property
Identity Property
Of Addition
Adding by 0 keeps the same
identity of the number
The process is adding
Answer: Identity Property of Addition
6/7
Name the property shown by the statement
Answer: Identity Property of Addition
6/7
Name the property shown by the statement
 
 
(11  4)  8 = 11  (4  8)
Write problem
Determine property
Associative Property
Of Multiplication
Numbers in same order but have
been regrouped with parenthesis
The process is multiplying
Answer: Associative Property of Multiplication
7/7
*
Name the property shown by the statement
Answer: Associative Property of Addition
7/7
Lesson 1:6
Assignment
Algebra: Properties
11 - 26 All