1. Properties of Operations
Objective: Identify properties of numbers

2. The Commutative Property
You can add and multiply real numbers in any order.
Numerically:
2 + 7 = 7 + 2
3 ● 9 = 9 ● 3
Algebraically:
a + b = b + a
ab = ba

3. The Commutative Property
Commute: to move to and from
Think of commuting to and from school. Just like you are moving from one place to the other, numbers can too!

4. The Associative Property
Parenthesis move, numbers do not move.
Numerically:
(6 + 8) + 2 = 6 + (8 + 2)
(7 ● 4) ● 5 = 7 ● (4 ● 5)
Algebraically:
(a + b) + c = a + (b + c)
(ab)c = a(bc)

5. The Associative Property
Associate: to keep company, as a friend
Think of associating with your friends: you hang out with them and stick together. Numbers in parentheses are grouped, or friends!

6. Commutative vs. Associative
Identify each property shown below.
1) = 4 + 7
Comm. Prop. Of Add. 2)
Assoc. Prop. Of Mult. 3)
Comm. Prop. Of Mult.
4) (4 + 2) + 3 = (2 + 4) + 3
Comm. Prop. Of Add.

7. Additive Identity Property Multiplicative Identity Property
The sum of a number and 0 is equal to the same
number. The number’s identity does not change.
Numerically: Algebraically:
= y = y
Multiplicative Identity Property
The product of a number and 1 is equal to the
same number. The number’s identity does not
change.
Numerically: Algebraically:
8 x 1 = (y)(1) = y

8. Zero Property Any number multiplied by zero equals zero.
Be careful not to mistake this for Identity Property!
5 x 0 = 0 a x 0 = 0

9. 2x ● 4y + 0 = 2x ● 4y
= - 9
7 x 1 = 7
1(3x + 4) = 3x + 4
Additive Identity
Multiplicative Identity

10. Identify the property being illustrated.
3 + 4 = 4 + 3
b. 5b ● 2c ● 0 = 0
c = -12
d. (x + 3) + 5 = x + (3 + 5)
Commutative Prop. of Add
Mult. Property of Zero.
Additive Identity
Associative Prop. of Add

11. Identify the property being illustrated.
h. 3d ● 4● 1 = 3d● 4
Additive Identity
Commutative Prop. of Mult.
Associative Prop. of Mult.
Multiplicative Identity Prop.

12. Identify the property being illustrated.
9b - 2c + 0 = 9b – 2c
2. 5 (-3b + 1) = -15b +5
(12 + 5) = ( ) + 5
pq = 2pq
Additive Identity
Distributive Prop.
Associative Prop. of Mult.

13. Identify the property being illustrated.
5. 9(mn) = (mn)9
6. 2(4x + 3) = 8x + 6
7. 4(ab) = (4a)b
8. 7xy ● 1 = 7xy
Commutative Prop. Of Mult.
Distributive Property
Associative Prop. of Mult.
Multiplicative Identity