1. Operations With Real Numbers SOL 7
Operations With Real Numbers SOL 7.3 by Lisa Beebe Chincoteague Combined School
Commutative Property
Associative Property
Distributive Property
Identity Properties
Inverse Properties
Multiplicative Property of Zero

2. Commutative Property (ORDER)
The order in which numbers are added or multiplied does not change the answer.
Examples:
3 + 5 = 5 + 3
Both sides equal 8.
2 · 7 = 7 · 2
Both sides equal 14.

3. Commutative Property

4. Associative Property (GROUPING)
The way in which three numbers are grouped with parentheses in addition or multiplication does not change the answer
Examples:
(1 + 2) + 3 = 1 + (2 + 3)
Both sides equal 6.
(2 · 3) · 5 = 2 · (3 · 5)
Both sides equal 30.

5. Associative Property

6. Distributive Property (Distribute)
States that the product of a number and the sum (or differences) of two other numbers equals the sum (or difference) of the products of the number and each other number
For any three numbers a, b, and c – it is true that a(b + c) = ab + ac

7. Distributive Property

8. Identity Property of Addition
A number plus zero is always itself.
Example:
= 11

9. Identity Property of Multiplication
A number multiplied by 1 is always itself
Example:
17 · 1 = 17

10. Additive Inverse Property
States that the sum of a number and its additive inverse always equals zero.
What you need to add to a number to get the identity
Example: = 0

11. Multiplicative Inverse Property
States that the product of a number and its multiplicative inverse (or reciprocal) always equals one
What you need to multiply to a number to get the identity
Example:
4 × ¼ = 1

12. Multiplicative Property of Zero
States that the product of any real number and zero is always zero.
Example: 5 × 0 = 0

13. Identify the following property: a + b = b + a
Commutative Property of Multiplicaton
Associative Property
Commutative Property of addition
Additive Identity Property 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

14. Which property is shown in the equation 26 + 0 = 26?
Inverse property of addition
Inverse property of multiplication
Identity property of addition
Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

15. Identity the following property: 5 · (x · y) = (5 · x) · y
Distributive Property
Associative property of multiplication
Associative Property of addition
Commutative property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

16. Identify the following property: 5 · (x · y) = 5 · (y · x)
Associative Property of Multiplication
Associative Property of Addition
Distributive Property
Commutative Property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

17. Which equation uses the distributive property?
-3(4 + 7) = -3(4) + -3(7)
-3(4 + 7) = -3(11)
-3(4 + 7) = -3(4) + 7
-3(4 + 7) = 4(-3) + 4(7) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

18. Which equation shows the multiplicative property of zero?
-35.9(1) = -35.9
-35.9(0) = 0
-35.9(359/10) = 1
-35.9(35.9) = 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

19. Which property is shown in the equation 7 × 0 = 0?
Additive identity property
Multiplicative Identity property
Multiplicative inverse property
Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

20. What is the identity for addition?-1 1
1/0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

21. What is the identity for multiplication?-1 1
1/0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

22. Which of the following is the additive inverse of 4?-4 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

23. Identify the property used. (1 + 3) × (4 + 1) = (1 + 3) × (1 + 4)
Associative property of multiplication
Associative property of addition
Commutative property of multiplication
Commutative property of addition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

24. Jessica has found that ¼ × 4/1 = 1
Jessica has found that ¼ × 4/1 = 1. She has discovered an example of _____________.
the multiplicative identity
the additive identity
a multiplicative inverse
an additive inverse 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

25. What is the reciprocal, or multiplicative inverse , of -3?
1/3
-1/3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

26. The expression x + (-x) = 0 demonstrates which property?
Multiplicative inverse
Distributive property
Additive inverse
Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

27. If the distributive property is applied to 5(7 + 3), which is the result?
5(7)(3)
5(7) + 3
5(7) + 5(3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30