1. Properties of Real Numbers
July 21, 2015

2. Objectives Identify the different properties of real numbers
Write the missing number in an equation where a principal has been applied
Simplify an expression by applying the property specified

3. Closure Property of Addition
The sum of two real number is a real number.
Example:
3 + 5 = 8
3 is real number, 5 is real number, the sum of 3 and 5 is real number

4. Closure Property of Multiplication
The product of two real number is a real number
Example:
3 x 5 = 15
3 is real number. 5 si real number. The product of 3 and 5 is real number.

5. Commutative Property of Addition=
7 + 5
5 + 7 =
3 + 8
8 + 3
4 + 6 = 6
+ 4
21 + = 13
13 + 21
If we change the order of the addends, will the sum change?
Changing the order of the addends does not affect the sum.
a + b = b + a

6. Commutative Property of Multiplication=
2 x 3
3 x 2 =
5 x 4
4 x 5
7 x 6 =
x 7 6
31 x = 11
11 x 31
If we change the order of the factors, does the product change?
Changing the order of the factors does not affect the product.
a x b = b x a

7. Associative Property of Addition?
( )
( ) = ?
3 + 9 = 8
+ 4 . = 12 12
Does the sum change as the grouping of the addends changes? ___ No

8. Associative Property of Addition?
( )
( ) = ?
9 + 12 = 16
+ 5 . 21 = 21
Changing the grouping of the addends does not change the sum
a + (b + c) = (a + b) + c

9. Associative Property of Addition? 7
6 + (7 + 3)
(6 + __) + 3 = ? 6 10 = 13 3
__ + __
__ + __ . 16 = 16 __ __
Changing the grouping of the addends does not change the sum
a + (b + c) = (a + b) + c

10. Associative Property of Addition? 2 9 3
__ + (9 + 3)
(2 + __) + __ = ? 2 12 = 11 3
__ + __
__ + __ . 14 = 14 __ __
Changing the grouping of the addends does not change the sum
a + (b + c) = (a + b) + c

11. Associative Property of Multiplication?
2 x 9 x 5
( )
( )
2 x 9 x 5 = ?
2 x 45 =
x 5 18 . = 90 90
Does the product change as the grouping of the factors changes? ___ No

12. Associative Property of Multiplication?
4 x 5 x 3
( )
( )
4 x 5 x 3 = ?
4 x 15 = 20
x 3 . 60 = 60
Changing the grouping of the factors does not change the product
a x (b x c) = (a x b) x c

13. Associative Property of Multiplication? 7
2 x (7 x 3)
(2 x __) x 3 = ? 2 21 = 14 3
__ x __
__ x __ . 42 = 42 __ __
Changing the grouping of the factors does not change the product
a x (b x c) = (a x b) x c

14. Associative Property of Multiplication? 8 5 6
__ x (5 x 6)
(8 x __) x __ = ? 8 30 = 40 6
__ x __
__ x __ .
240 =
240 __ __
Changing the grouping of the factors does not change the product
a x (b x c) = (a x b) x c

15. Distributive Property of Multiplication with Respect to Addition
2 x (8 + 5)
2 x (8 + 5)
(2 x 8) +
(2 x 5)
2 x 16 + 10 13 26 26
What number was multiplied by 8 and 5?
What operations are involved in the equation?
Did you get the same answer?

16. Distributive Property of Multiplication with Respect to Addition
7 x (3 + 4)
7 x (3 + 4)
(7 x 3) +
(7 x 4) 21 + 28
7 x 7 49 49
We can break one of the factors as the sum of addends, multiply each of these addends by the factor then add their products
a x (b + c) = (a x b) + (a x c)

17. Distributive Property of Multiplication with Respect to Addition
7 x (9 + 3) 7 9 7 3
7 x (9 + 3)
(_ x _) +
(_ x _) 7 12 63 21
__ x __
__ + __ 84 84 __ __
We can break one of the factors as the sum of addends, multiply each of these addends by the factor then add their products
a x (b + c) = (a x b) + (a x c)

18. Identity Property of Addition=
7 + 0 7 =
0 + 8 8
4 + 0 = 4
21 + = 21
If we change the order of the addends, will the sum change?
The sum of zero and a number or vice versa is equal to the number itself
a + 0 = a
zero
The identity element for addition is ____

19. Identity Property of Multiplication=
7 x 1 7 =
1 x 43 43
79 x 1 = 79
83 x = 1 83
If we change the order of the addends, will the sum change?
The product of one and a number or vice versa is equal to the number itself
a x 1 = a
one
The identity element for multiplication is ____

20. Inverse Property of Addition
For each real number a there exists a unique real number –a such that their sum is zero.
a + (-a) = 0
In other words opposites add to zero.

21. Inverse Property of Multiplication
For each real number a there exists a unique real number such that their product is 1.

22. Let’s play “Name that property!”

23. Commutative Property of Addition2.
Which Property?
3 + 7 = 7 + 3
Commutative Property of Addition

24. Identity Property of Addition3.
Which Property?
8 + 0 = 8
Identity Property of Addition

25. Commutative Property of Multiplication5.
Which Property?
6 • 4 = 4 • 6
Commutative Property of Multiplication

26. Inverse Property of Addition6.
Which Property?
17 + (-17) = 0
Inverse Property of Addition

27. Commutative Property of Multiplication7.
Which Property?
2(5) = 5(2)
Commutative Property of Multiplication

28. Associative Property of Addition1.
Which Property?
(2 + 1) + 4 = 2 + (1 + 4)
Associative Property of Addition

29. Closure Property of Addition8.
Which Property?
even + even = even
Closure Property of Addition

30. 9.
Which Property?
3(2 + 5) = 3•2 + 3•5
Distributive Law

31. Identity Property of Multiplication
14.
Which Property?
1(-9) = -9
Identity Property of Multiplication

32. Inverse Property of Addition
15.
Which Property?
3 + (-3) = 0
Inverse Property of Addition

33. Associative Property of Addition
16.
Which Property?
1 + [-9 + 3]
= [1 + (-9)] + 3
Associative Property of Addition

34. Commutative Property of Multiplication
17.
Which Property?
-3(6) = 6(-3)
Commutative Property of Multiplication

35. Identity Property of Addition
18.
Which Property?
= -8
Identity Property of Addition

36. Commutative Property of Addition
21.
Which Property?
7 + (-5) =
Commutative Property of Addition

37. 2) 9 + (12 + 4) = ___________ APA 3) 35 x 1 = __________ IPM
Complete each equation using the indicated property.
1) = _________ CPA
2) 9 + (12 + 4) = ___________ APA
3) 35 x 1 = __________ IPM
4) 3 x (8 + 7) = ____________ DL
5) 32 x 56 = ________ CPM
21 + 4
(9 + 12) + 4 35
(3 x 8) + (3 x 7)
56 x 32