# Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

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Properties of Real Numbers CommutativeAssociativeDistributive 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 Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 5 = 5 4 or ab = ba. 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 such that their product is 1.

Lets 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

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

8 + 0 = 8 Identity Property of Addition 3.

6 4 = 4 6 Commutative Property of Multiplication 5.

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

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

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

even + even = even Closure Property 8.

3(2 + 5) = 32 + 35 Distributive Property 9.

6(78) = (67)8 Associative Property of Multiplication 10.

5 1 = 5 Identity Property of Multiplication 11.

(6 – 3)4 = 64 – 34 Distributive Property 13.

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

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

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

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

-8 + 0 = -8 Identity Property of Addition 18.

37 – 34 = 3(7 – 4) Distributive Property 19.

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

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

(5 + 4)9 = 45 + 36 Distributive Property 22.

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

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

5 1 / 7 + 0 = 5 1 / 7 Identity Property of Addition 25.

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

1 2 / 5 1 = 1 2 / 5 Identity Property of Multiplication 27.

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

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

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

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

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

ab = ba Commutative Property of Multiplication 33.

a + 0 = a Identity Property of Addition 34.

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

a1 = a Identity Property of Multiplication 36.

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

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

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

a + (-a) = 0 Inverse Property of Addition 40.

Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

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