Download Commutative Property

1-6 Properties
Warm Up
Evaluate.
1. 2 + 5  3 – 7
10
2. 5(3 – 1) ÷ (3 + 2) 2
3. (4 + 1)2 – 8 ÷ 2
21
4. 12 ÷ 3  6 – 20
4
Course 2
1-6 Properties
Learn how to identify properties of
rational numbers and use them to
simplify numerical expressions.
Course 2
1-6 Properties
Vocabulary
Commutative Property
Associative Property
Identity Property
Distributive Property
Course 2
1-6 Properties
Commutative Property: allows you to add or
multiply in any order. (order is switched)
Example: 4 + 8 = 8 + 4
3·9=9·3
Course 2
1-6 Properties
Associative Property: When you add or multiply
you can regroup the numbers in any combination.
(regrouping)
Example: ( 4 + 5 ) + 1 = 4 + ( 5 + 1 )
(9 · 2 ) · 6 = 9 · ( 2 · 6 )
Course 2
1-6 Properties
Identity Property: the sum of 0 and any number
is the number, and the product of 1 and any
number is the number.(one of the factors is 0 or 1)
Example: 4 + 0 = 4
8·1=8
Course 2
1-6 Properties
Example 1
Tell which property is represented.
A. (2  6)  1 = 2  (6  1)
The numbers are regrouped.
Associative Property
B. 3 + 0 = 3
One of the factors is 0.
Identity Property
C. 7 + 9 = 9 + 7
Commutative Property
Course 2
The order of the variables is
switched.
1-6 Properties
Example 2
Tell which property is represented.
A. 7  1 = 7
One of the factors is 1.
Identity Property
B. 3 + 4 = 4 + 3
Commutative Property
The order of the numbers is
switched.
C. (5  1)  2 = 5  (1  2)
The numbers are regrouped.
Associative Property
Course 2
1-6 Properties
Example 3 - Lets work these together.
Simplify each expression. Justify each step.
A. 21 + 16 + 9
21 + 16 + 9 = 16 + 9 + 21
= 16 + (9 + 21)
= 16 + 30
B. 20  9  5 = 46
20  9  5 = 20  5  9
= 20  (5  9)
= 20  45
= 900
Course 2
Commutative Property.
Associative Property.
Add.
Commutative Property.
Associative Property.
Multiply.
1-6 Properties
Example 4 – You try!
Simplify each expression. Justify each step.
A. 17 + 14 + 3
17 + 14 + 3 = 14 + 17 + 3
= 14 + (17 + 3)
B. 12  3  5
= 14 + 20
= 34
12  3  5 = 3  5  12
= 3  (5  12)
= 3  60
= 180
Course 2
Commutative Property.
Associative Property.
Add.
Commutative Property.
Associative Property.
Multiply.
1-6 Properties
You can use the Distributive Property to multiply
numbers mentally by breaking apart one of the
numbers and writing it as a sum or difference.
Course 2
1-6 Properties
Example 5
Use the Distributive Property to find 6(54).
Method 1:
6(54) = 6(50 + 4)
= 300 + 24
Use the Distributive
Property.
Multiply.
= 324
Add.
= (6  50) + (6  4)
Course 2
Rewrite 54 as 50 + 4.
1-6 Properties
Example 6
Use the Distributive Property to find 8(19).
Method 1:
8(19) = 8(10 + 9)
= (8  10) + (8  9)
Course 2
Rewrite 19 as 10 + 9.
Use the Distributive
Property.
= 80 + 72
Multiply.
= 152
Add.
1-6 Properties
Summary
Tell which property is represented.
1. 17  1 = 17
Identity Property
Associative Property
3. 2  16 = 16  2 Commutative Property
2. (12 + 14) + 5 = 12 + (14 + 5)
Simplify each expression. Justify each step.
4. 4  12  25
1,200
5. 48 + (15 + 2)
65
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9
Course 2
102
117