# Properties of Addition and Multiplication Why is it important to recognize these properties? It helps us with mental math. It helps us recognize patterns.

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Properties of Addition and Multiplication Why is it important to recognize these properties? It helps us with mental math. It helps us recognize patterns in problems. It helps us solve problems faster!!!

Inverse Operation Property Inverse means opposite. Use the opposite operation to check solutions and find the value of variables. Addition X+4=9 Multiplication 8*x=32

Commutative Property If the order of the addends or factors is changed, the sum or product stays the same. Addition 4+9=9+4 Multiplication 2x8=8x2

Associative Property The way addends are grouped or factors are grouped does not change the sum or product. Addition (8+1)+5=8+(1+5) Multiplication (6x2)x4=6x(2x4)

Identity Property The sum of zero and any number equals that number. The product of one and any number equals that number. Addition 6+0=6 Multiplication 5x1=5

Distributive Property Multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. Multiplication 3x(5+10)=(3x5)+(3x10)

Zero Property of Multiplication The product of any number and zero is zero. Multiplication 12x0=0

by D. Fisher

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

3 + 7 = 7 + 3 Commutative Property of Addition

8 + 0 = 8 Identity Property of Addition

6 4 = 4 6 Commutative Property of Multiplication

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

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

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

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

5 1 = 5 Identity Property of Multiplication

(6 – 3)4 = 64 – 34 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 Addition

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

-8 + 0 = -8 Identity Property of Addition

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

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

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

(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

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

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

ab = ba Commutative Property of Multiplication

a + 0 = a Identity Property of Addition

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

a1 = a Identity Property of Multiplication

a +b = b + a Commutative Property of Addition

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

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

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

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