1. Properties of Real Numbers
Commutative Property
Think… commuting to work.
Deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY.
a+b = b+a
4 • 6 = 6 • 4

2. Properties of Real Numbers
Associative Property
Think…the people you associate with, your group.
Deals with grouping when you Add or Multiply.
Order does not change.

3. Properties of Real Numbers
Associative Property
(a + b) + c = a + ( b + c)
(nm)p = n(mp)

4. Properties of Real Numbers
Additive Identity Property
s + 0 = s
Multiplicative Identity Property
1(b) = b

5. Properties of Real Numbers
Additive Inverse Property
a + (-a) = 0
Multiplicative Inverse Property
a∙( ) = 1, a 0

6. Properties of Real Numbers
Distributive Property
a(b + c) = ab + ac
(r + s)9 = 9r + 9s

7. Name the Property 5 = 5 + 0 5(2x + 7) = 10x + 35 8 • 7 = 7 • 8
24(2) = 2(24)
(7 + 8) + 2 = 2 + (7 + 8)
Additive Identity
Distributive
Commutative

8. Name the Property Associative 7 + (8 + 2) = (7 + 8) + 2 Multiplicative
Identity
Distributive
7 + (8 + 2) = (7 + 8) + 2
1 • v + -4 = v + -4
(6 - 3a)b = 6b - 3ab
4(a + b) = 4a + 4b

9. Properties of Real Numbers
Reflexive Property
a + b = a + b
The same expression is written on both sides of the equal sign.

10. Properties of Real Numbers
Symmetric Property
If a = b then b = a
If = 9 then 9 = 4 + 5

11. Properties of Real Numbers
Transitive Property
If a = b and b = c then a = c
If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

12. Properties of Real Numbers
Substitution Property
If a = b, then a can be replaced by b.
a(3 + 2) = a(5)

13. Name the property Distributive Substitution Reflexive Symmetric
5(4 + 6) =
5(4 + 6) = 5(10)
5(4 + 6) = 5(4 + 6)
If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6)
5(4 + 6) = 5(6 + 4)
If 5(10) = 5(4 + 6) and 5(4 + 6) = then 5(10) =
Distributive
Substitution
Reflexive
Symmetric
Commutative
Transitive