 # Properties of Real Numbers

## Presentation on theme: "Properties of Real Numbers"— Presentation transcript:

Properties of Real Numbers
Commutative Associative Identity + × Inverse + × Zero Property Reflexive Distributive

Commutative Properties
Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: = or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

Verbal Hints for Commutative Property
Commute Switch Places Move to a new location

Associative Properties
Changing the grouping of the numbers in addition or multiplication will not change the result. Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

Verbal Hints for Associative Property
Regroup They simply group with a new friend ( ) change places but numbers stay the same

There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

Multiplicative Identity Property
There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

Verbal Hints for Identity Property
The value that returns the input unchanged Remember “I” in the word identity

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.

Opposite numbers Same number but different sign Zero Pairs

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

Verbal Hints for Multiplicative Inverse
Flip the number Reciprocal

Zero Property of Multiplication
Any number multiplied by 0 is equal to 0 A ● 0 = 0 -23 ● 0 = 0 ½ ● 0 = 0 0.25 ● 0 = 0 “zero times any value is 0

A real number is always equal to itself
Reflexive Property A number is always equal to itself A = A -2 = -2 5 = 5 A real number is always equal to itself

Distributive Property

Verbal Hints for Distributive Property
Multiplication distributes across addition or subtraction. Multiply across the parentheses!!!!!

Let’s play “Name that property!”

State the property or properties that justify the following.
3 + 2 = 2 + 3 Commutative Property

State the property or properties that justify the following.
10(1/10) = 1 Multiplicative Inverse Property

State the property or properties that justify the following.
3(x – 10) = 3x – 30 Distributive Property

State the property or properties that justify the following.
3 + (4 + 5) = (3 + 4) + 5 Associative Property

State the property or properties that justify the following.
(5 + 2) + 9 = (2 + 5) + 9 Commutative Property

2. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

3. Which Property? 8 + 0 = 8 Identity Property of Addition

Commutative Property of Multiplication
5. Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication

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

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

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

8. Which Property? even + even = even Closure Property

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

Associative Property of Multiplication
10. Which Property? 6(7•8) = (6•7)8 Associative Property of Multiplication

Identity Property of Multiplication
11. Which Property? 5 • 1 = 5 Identity Property of Multiplication

Properties Using Negatives

Distributive Property
13. Which Property? (6 – 3)4 = 6•4 – 3•4 Distributive Property

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

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

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

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

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

Distributive Property
19. Which Property? 3•7 – 3•4 = 3(7 – 4) Distributive Property

20. Which Property? 6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition

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

Distributive Property
22. Which Property? (5 + 4)9 = Distributive Property

Associative Property of Multiplication
23. Which Property? -3(5 • 4) = (-3 • 5)4 Associative Property of Multiplication

Commutative Property of Multiplication
24. Which Property? -8(4) = 4(-8) Commutative Property of Multiplication

Properties Using Fractions

25. Which Property? 51/7 + 0 = 51/7 Identity Property of Addition

26. Which Property? 3/4 – 6/7 = – 6/7 + 3/4 Commutative Property of Addition

Identity Property of Multiplication
27. Which Property? 12/5 • 1 = 12/5 Identity Property of Multiplication

(fraction)(fraction) = fraction
28. Which Property? (fraction)(fraction) = fraction Closure Property

29. Which Property? -8 2/5 + 0 = -8 2/5 Identity Property of Addition

Associative Property of Multiplication
30. Which Property? [(-2/3)(5)]9 = -2/3[(5)(9)] Associative Property of Multiplication

Properties Using Variables

Distributive Property
31. Which Property? 6(3 – 2n) = 18 – 12n Distributive Property

32. Which Property? 2x + 3 = 3 + 2x Commutative Property of Addition

Commutative Property of Multiplication
33. Which Property? ab = ba Commutative Property of Multiplication

34. Which Property? a + 0 = a Identity Property of Addition

Associative Property of Multiplication
35. Which Property? a(bc) = (ab)c Associative Property of Multiplication

Identity Property of Multiplication
36. Which Property? a•1 = a Identity Property of Multiplication

37. Which Property? a +b = b + a Commutative Property of Addition

Distributive Property
38. Which Property? a(b + c) = ab + ac Distributive Property

39. Which Property? a + (b + c) = (a +b) + c Associative Property of Addition