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 PropertyInverse means opposite. Use the opposite

operation to check solutions and find the value of variables.

•AdditionX+4=9

•Multiplication8*x=32

Commutative PropertyIf the order of the addends or factors is

changed, the sum or product stays the same.

•Addition4+9=9+4

•Multiplication2x8=8x2

Associative PropertyThe 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 PropertyThe sum of zero and any number equals that number. The product of one and any number

equals that number. •Addition

6+0=6

•Multiplication5x1=5

Distributive PropertyMultiplying a sum by a number is the same as

multiplying each addend in the sum by the number and then adding the products.

•Multiplication3x(5+10)=(3x5)+(3x10)

Zero Property of MultiplicationThe product of any number and zero is zero.

•Multiplication12x0=0

by D. Fisher

(2 + 1) + 4 = 2 + (1 + 4)

Associative Property Associative Property of Additionof Addition

3 + 7 = 7 + 3

Commutative Commutative Property of AdditionProperty of Addition

8 + 0 = 8

Identity Property of Identity Property of AdditionAddition

6 • 4 = 4 • 6

Commutative Property Commutative Property of Multiplicationof Multiplication

17 + (-17) = 0

Inverse Property of Inverse Property of AdditionAddition

2(5) = 5(2)

Commutative Property Commutative Property of Multiplicationof Multiplication

3(2 + 5) = 3•2 + 3•5

Distributive PropertyDistributive Property

6(7•8) = (6•7)8

Associative Property of Associative Property of MultiplicationMultiplication

5 • 1 = 5

Identity Property of Identity Property of MultiplicationMultiplication

(6 – 3)4 = 6•4 – 3•4

Distributive PropertyDistributive Property

1(-9) = -9

Identity Property of Identity Property of MultiplicationMultiplication

3 + (-3) = 0

Inverse Property of Inverse Property of AdditionAddition

1 + [-9 + 3]

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

AdditionAddition

-3(6) = 6(-3)

Commutative Property Commutative Property of Multiplicationof Multiplication

-8 + 0 = -8

Identity Property of Identity Property of AdditionAddition

3•7 – 3•4 = 3(7 – 4)

Distributive PropertyDistributive Property

6 + [(3 + (-2)]

= (6 + 3) + (- 2)Associative Property Associative Property

of Additionof Addition

7 + (-5) = -5 + 7

Commutative Commutative Property of AdditionProperty of Addition

(5 + 4)9 = 45 + 36

Distributive PropertyDistributive Property

-3(5 • 4) = (-3 • 5)4

Associative Property of Associative Property of MultiplicationMultiplication

-8(4) = 4(-8)

Commutative Property Commutative Property of Multiplicationof Multiplication

6(3 – 2n) = 18 – 12n

Distributive PropertyDistributive Property

2x + 3 = 3 + 2x

Commutative Property Commutative Property of Additionof Addition

ab = ba

Commutative Property Commutative Property of Multiplicationof Multiplication

a + 0 = a

Identity Property of Identity Property of AdditionAddition

a(bc) = (ab)c

Associative Property of Associative Property of MultiplicationMultiplication

a•1 = a

Identity Property of Identity Property of MultiplicationMultiplication

a +b = b + a

Commutative Property Commutative Property of Additionof Addition

a(b + c) = ab + ac

Distributive PropertyDistributive Property

a + (b + c) = (a +b) + c

Associative Property of Associative Property of AdditionAddition

a + (-a) = 0

Inverse Property of Inverse Property of AdditionAddition