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The Identity Property Using this property means you can operate with a number (multiply by 1 or add 0) and the number will keep its identity (stay the same)
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Do as many as you can in 5 minutes
17 21 25 2
6
1,000,000 7
2
17
64
81
84
Properties of Rational Numbers
Learning Goals (you will be tested on both of these Friday!):
1. I will be able to identify the Associative, Distributive, Commutative and Identity Properties.
2. I will understand how to apply the properties when doing problems.
The Identity Property Using this property means you can operate with a number(multiply by 1 or add 0)and the number will keep its identity (stay the same)
Identity Property… of Addition5 + 0 = 5of Multiplication3 1 = 3
The Commutative PropertyCommute commonly means drive to work!
This property says that the numbers in addition or multiplication problems can move around but the answer will stay the same.
How we use the Commutative Property…
(numbers trade places)in Addition
18 + 7 + 2 = 18 + 2 + 7in Multiplication
25 9 4 = 25 4 9
Why is this helpful ???
The Associative PropertyYour friends (or group) are the people with whom you associate!
For addition or multiplication, you can change the groups and the answer stays the same.
How we use the Associative Property… (groups change)
in Addition
(74 + 8) + 12 = 74 + (8 + 12)
in Multiplication
(3 4) 25= 3 (4 25)
Why is this helpful ???
The Distributive PropertyDistribute means to pass something out or deliver it!
We can break a number into smaller pieces and distribute it across the operation without changing the answer!
How we use the Distributive Property
(break the number and use the parts)
7(43) = 7(40 + 3) = 7(40) + 7(3) = 280 + 21 = 301 Why is
this helpful ???
Which Property is this?
99 + 0 = 991 - Identity2 - Associative3 - Commutative4 - Distributive
Identity Property (of
Addition)
Which Property?
5(20 + 7) = 100 + 35
1 - Identity2 - Associative3 - Commutative4 - Distributive
The Distributive Property
Which Property?
21 + 6 = 6 + 21
Commutative Property
(of Addition)
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
11 + 0 = 111 - Identity2 - Associative3 - Commutative4 - Distributive
Identity Property
(of Addition)
Which Property?
(10 3) 7 = 10 (3 7)
Associative Property
(of Multiplication)
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
4(n - 8) = 4n - 32
The Distributive Property
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
(34)(6)=(6)(34)
Commutative Property
(of Multiplication)
1 - Identity2 - Associative3 - Commutative4 - Distributive
How we use the Commutative Property…
(numbers trade places)in Addition
18 + 7 + 2 = 18 + 2 + 7in Multiplication
25 9 4 = 25 4 9
Why is this helpful ???
Applying the Properties!Use the Commutative Property to
make this problem easier…
63 + 49 + 7 + 51
63 + 7 + 49 + 51 70 + 100 = 170
How we use the Associative Property… (groups change)
in Addition
(74 + 8) + 12 = 74 + (8 + 12)
in Multiplication
(3 4) 25= 3 (4 25)
Why is this helpful ???
Use the Associative Property to make this problem easier…
(37∙5)∙20 = 37∙(5∙20) = 37∙100 = 3700
Applying the Properties!
How we use the Distributive Property
(break the number and use the parts)
7(43) = 7(40 + 3) = 7(40) + 7(3) = 280 + 21 = 301 Why is
this helpful ???
Use the Distributive Property to make this problem easier…
98∙6 =90 ∙6 = 8 ∙6 =
Applying the Properties!
540 48588
Use the Associative Property to make this problem easier…
47 + (3 + 29) + 1(47 + 3) + (29 + 1) 50 + 30
80
Applying the Properties!
Applying the PropertiesUse the Distributive Property to
make this problem easier…
49∙11 = 49∙1049∙1
= 490= 49
539
Use the Commutative Property to make this problem easier…
4∙89∙25
=4∙25∙89 = 100∙89 = 8900
Applying the Properties!
Homework Time!P30 #1-18, 65-68
Use the Commutative Property to make this problem easier…
Applying the Properties!
Which Property?
(8 + 4) + 1 = 8 + (4 + 1)
Associative Property (of Addition)
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
3 9 = 9 3
Commutative Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
3 + 4 = 4 + 3
Commutative Property of Addition
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
3 1 = 3
Identity Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
5(9w + 1) = 45w + 5
The Distributive Property
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
(2 + 6) + 3 = 2 + (6 + 3)
Associative Property of Addition
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
14 2 = 2 14Commutative
Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
9 1 = 9
Identity Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
3(6k - 9) = 18k - 27
The Distributive Property
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
11 + 0 = 11
Identity Property of Addition
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
4 2 = 2 4
Commutative Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
(4 + 7)(9)=(9)(4 +7)
Commutative Property of Multiplication
1 - Identity2 - Associative3 - Commutative4 - Distributive
Which Property?
(4 + 7) + 2= (7 + 4) + 2
Commutative Property of Addition
1 - Identity2 - Associative3 - Commutative4 - Distributive
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