Properties of Real Numbers Commutative Associative Distributive Identity
Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×
Commutative Properties Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.
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)
Distributive Property Multiplication distributes over addition.
Additive Identity Property 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.
Additive Inverse Property 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.
Multiplicative Inverse Property For each real number a there exists a unique real number product is 1. such that their
Let’s play “Name that property!”
State the property or properties that justify the following. 3+2=2+3
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
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) = 3 x – 30
State the property or properties that justify the following. 3(x – 10) = 3 x – 30 Distributive Property
State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5
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
State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property
3+7=7+3
3+7=7+3 Commutative Property of Addition
8+0=8
8+0=8 Identity Property of Addition
6 • 4=4 • 6 Commutative Property of Multiplication
17 + (-17) = 0
17 + (-17) = 0 Inverse Property of Addition
2(5) = 5(2)
2(5) = 5(2) Commutative Property of Multiplication
(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition
even + even = even
3(2 + 5) = 3 • 2 + 3 • 5 Distributive Property
6(7 • 8) = (6 • 7)8 Associative Property of Multiplication
5 • 1=5 Identity Property of Multiplication
(6 – 3)4 = 6 • 4 – 3 • 4 Distributive Property
1(-9) = -9 Identity Property of Multiplication
3 + (-3) = 0 Inverse Property of Addition
![1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of](http://slidetodoc.com/presentation_image/2f2128f3c54cceb656c00a1256118467/image-47.jpg "1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of")
1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition
-3(6) = 6(-3) Commutative Property of Multiplication
-8 + 0 = -8 Identity Property of Addition
3 • 7 – 3 • 4 = 3(7 – 4) Distributive Property
![6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property](http://slidetodoc.com/presentation_image/2f2128f3c54cceb656c00a1256118467/image-55.jpg "6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property")
6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition
7 + (-5) = -5 + 7 Commutative Property of Addition
(5 + 4)9 = 45 + 36
(5 + 4)9 = 45 + 36 Distributive Property
-3(5 • 4) = (-3 • 5)4 Associative Property of Multiplication
-8(4) = 4(-8) Commutative Property of Multiplication
1 5/ + 0 = 7 1 5/ 7
1 5/ + 0 = 7 1 5/ 7 Identity Property of Addition
3/ – 4 6/ = – 7 6/ + 7 3/ 4 Commutative Property of Addition
2 1/ • 1 = 5 2 1/ 5
2 1/ • 1 = 5 2 1/ 5 Identity Property of Multiplication
-8 2/ + 0 = -8 5 2/ 5
-8 2/ + 0 = -8 5 2/ 5 Identity Property of Addition
![2 [(- / )(5)]9 = 3 2 -/ [(5)(9)] 3 Associative Property of Multiplication](http://slidetodoc.com/presentation_image/2f2128f3c54cceb656c00a1256118467/image-74.jpg "2 [(- / )(5)]9 = 3 2 -/ [(5)(9)] 3 Associative Property of Multiplication")
2 [(- / )(5)]9 = 3 2 -/ [(5)(9)] 3 Associative Property of Multiplication
6(3 – 2 n) = 18 – 12 n
6(3 – 2 n) = 18 – 12 n Distributive Property
2 x + 3 = 3 + 2 x
2 x + 3 = 3 + 2 x Commutative Property of Addition
ab = ba
ab = ba Commutative Property of Multiplication
a+0=a
a+0=a Identity Property of Addition
a(bc) = (ab)c
a(bc) = (ab)c Associative Property of Multiplication
a • 1 = a Identity Property of Multiplication
a +b = b + a Commutative Property of Addition
a(b + c) = ab + ac
a(b + c) = ab + ac Distributive Property
a + (b + c) = (a +b) + c Associative Property of Addition
a + (-a) = 0 Inverse Property of Addition
Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×
- Slides: 96
