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Objective
Use the Commutative, Associative,
Identity, and Distributive Properties
Vocabulary
None
Properties
Property
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(b + c) = ab + ac
4(6 + 2) = 4(6) + 4(2)
a(b - c) = ab - ac
3(7 - 5) = 3(7) - 3(5)
a+0=a
9+0=9
a·1=a
5·1=5
If 2 + 4 = 6 and 6 = 3 · 2, then 2 + 4 = 3 ·
2
Commutative
(Change position of numbers)
Associative
(Regroup numbers)
Distributive
(Distribute numbers)
Identity Additive
Multiplicative
Transitive
if a = b and b = c, then a = c
Example 1 Use the Distributive Property
Example 2 Apply the Distributive Property
Example 3 Identify Properties
Example 4 Identify Properties
Example 5 Apply Properties
Find 6  43 using the Distributive Property
6  43
Write the problem
6 (40 + 3)
Write 43 as
6(40) + 6(3)
Bring down 6
Use the Distributive Property
Distribute the 6 to the 40
Bring down +
Distribute the 6 to the 3
1/4
Find 6  43 using the Distributive Property
6  43
6 (40 + 3)
Follow Order of Operations
P
E
MD
AS
Multiply from left to right
6(40) + 6(3)
240 + 18
Bring down +
Add
Answer: 258
1/4
Find 7  33 using the Distributive Property.
Answer: 231
1/4
Identify the property shown by the equation
3+2=2+3
Answer:
Commutative Property
of Addition
Write the problem
Identify what is happening to
the numbers
Begins with 3 + 2
Ends with 2 + 3
Changed position of numbers
Identify property
Identify process
2/4
Identify the property shown by the equation 9  6 = 6  9
Answer: Commutative Property of Multiplication
2/4
Identify the property shown by the equation
(13  3)  4 = 13  (3  4)
(13  3)  4 = 13  (3  4)
Write the problem
Identify what is happening to
the numbers
Answer:
Associative Property
of Multiplication
Begins with (13  3)  4
Ends with 13  (3  4)
Regrouping numbers
Identify property
Identify process
3/4
Identify the property shown by the equation
(10 + 7) + 4 = 10 + (7 + 4)
Answer: Associative Property of Addition
3/4
Find 12  2  4 using the Commutative Property and
the Associative Property
12  2  4
2  4  12
(2  4)  12
Write the problem
Since you can easily multiply 2
and 4, change the order by
using the Commutative Property
Now use the Associative
Property by using parenthesis
around the 2  4
4/4
Find 12  2  4 using the Commutative Property and
the Associative Property
12  2  4
2  4  12
(2  4)  12
8  12
Follow Order of Operations
P
E
MD
AS
Work inside parenthesis
Multiply
Answer: 96
4/4
*
Find
using the Commutative Property and
Associative Property
Answer: 117
4/4
Assignment
Lesson 9:1
Properties
19 - 42 All
THEME PARKS Suppose admission to a theme park
costs $35 per person and meals cost $20 per person.
What is the cost for a family of 5 people?
Find the cost of 5 admissions and 5 meals.
Then add.
cost of 5 admissions
cost of 5 meals
Answer: The total cost is $275.
2/5
BOWLING Suppose the cost of bowling three games at
a local bowling alley is $6.50 and the cost of shoe rental
is $1.50. What is the cost for a group of 6 friends to
each rent a pair of shoes and bowl three games?
Answer: $48
2/5