1. Properties

2. Commutative Property Think ….Order
The order of the numbers doesn’t change the result (answer to the problem)
a + b = b + a = 2 + 6
p X q = q X p 6 x 2 = 2 x 6

3. Associative Property Think “Grouping”
The grouping doesn’t change the answer.
(p+q) + r = p + ( q + r)
(2 + 3) + 4 = 2 + (3 + 4)
(p X q) X r = p X (q X r)
(5 x 6) x 7 = 5 x (6 x 7)

4. Identity Property of Multiplication
Any number multiplied by 1 will give you the original number.
23,487 X 1 = 23,487
a x 1 = a

5. Identity Property of Addition
Any number added to 0 will give you the original number.
23, = 23,487
a + 0 = a

6. Zero Property of Multiplication
When any number is multiplied with zero, the answer is zero.
98,756,432 X 0 = 0

7. Distributive Property
Multiplying the sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the product.
9 X (20 - 3) = (9 X 20) – (9 X 3)
8 X (40 + 5) = (8 X 40) + (8 X 5)
8 X 45 = (8 X 40) + (8 X 5)

8. Distributive Property Examples
4 X 509 = (4 X 500) + (4 X m)
6 (5 + 8)= (6 X n) + (6 X 8)
s (4 + 9)= (5 X 4) + (5 X 9)

9. Inverse Property of Addition
The sum of any integer and its additive inverse is 0.
a + (-a) = 0
3+ (-3) = 0

10. Multiplicative Inverse Property
The product of a nonzero number and its reciprocal, or multiplicative inverse, is 1.
NUMBERS
ALGEBRA

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

17. Properties of Equality
Symmetric Property
If a = b then b = a
If = 9 then 9 = 4 + 5

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

19. Substitution Property
If a = b, then a can be replaced by b.
a(3 + 2) = a(5)

20. 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