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

6. • 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
Commutative
Commutative
Name the Property

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

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

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

10. 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

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

12. Name the property
• 5(4 + 6) = 20 + 30
• 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) = 20 + 30 then
5(10) = 20 + 30
• Distributive
• Substitution
• Reflexive
• Symmetric
• Commutative
• Transitive