1. Properties of Real Numbers

2. Reciprocals
2 numbers whose product is 1 are reciprocals of each other.

3. Absolute Value
The absolute value of a number is its distance from 0 on the number line. The absolute value of x is written
Examples of absolute value:

4. Inverse Property Of Multiplication
States that reciprocals multiply to 1.

5. Inverse Property of Addition
States that opposites add to zero.
7 + (-7) = 0 and = 0

6. Inverse Properties of the Operations
Addition is the inverse of subtraction.
Subtraction is the inverse of addition.
Division is the inverse of multiplication.
Multiplication is the inverse of division.

7. Commutative Property of Addition
a + b = b + a
When adding two numbers, the order of the numbers does not matter.
Examples:
2 + 3 = (-5) + 4 = 4 + (-5)

8. Commutative Property of Multiplication
a  b = b  a
When multiplying two numbers, the order of the numbers does not matter.
Examples:
2  3 = 3  2 (-3)  24 = 24  (-3)

9. Associative Property of Addition
a + (b + c) = (a + b) + c
When 3 numbers are added, it makes no difference which 2 numbers are added 1st.
Examples:
2 + (3 + 5) = (2 + 3) + 5
(4 + 2) + 6 = 4 + (2 + 6)

10. Associative Property of Multiplication
a(bc) = (ab)c
When 3 numbers are multiplied, it makes no difference which 2 numbers are multiplied 1st.
Examples:
2  (3  5) = (2  3)  5
(4  2)  6 = 4  (2  6)

11. Distributive Property
a(b + c) = ab + ac
Multiplication distributes over addition.
Examples of the Distributive Property
2 (3 + 5) = (2  3) + (2  5)
(4 + 2)  6 = (4  6) + (2  6)

12. Identity Property of Addition
If 0 is added to a number, the result is that number.
Example: = = 3

13. Identity Property of Multiplication
If a number is multiplied by 1, the result is that number.
Example: 5  1 = 1  5 = 5

14. Identify which property that justifies each of the following.
4  (8  2) = (4  8)  2

15. Identify which property that justifies each of the following.
4  (8  2) = (4  8)  2
Associative Property of Multiplication

16. Which Property??
6 + 8 = 8 + 6

17. Commutative Property of Addition
6 + 8 = 8 + 6
Commutative Property of Addition

18. Which Property??
= 12

19. Additive Identity Property
= 12
Additive Identity Property

20. Which Property?
5(2 + 9) = (5  2) + (5  9)

21. Distributive Property
5(2 + 9) = (5  2) + (5  9)
Distributive Property

22. Which Property?
5 + (2 + 8) = (5 + 2) + 8

23. Associative Property of Addition
5 + (2 + 8) = (5 + 2) + 8
Associative Property of Addition

24. Identify which property that justifies each of the following.

25. Identify which property that justifies each of the following.
Multiplicative Inverse Property

26. Which Property?
5  24 = 24  5

27. Commutative Property of Multiplication
5  24 = 24  5
Commutative Property of Multiplication

28. Which Property??
= 0

29. Additive Inverse Property
= 0
Additive Inverse Property

30. -34 1 = -34

31. Multiplicative Identity Property
-34 1 = -34
Multiplicative Identity Property