properties of addition and multiplication why is it important to recognize these properties? it...
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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!!!
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Inverse Operation PropertyInverse means opposite. Use the opposite
operation to check solutions and find the value of variables.
•AdditionX+4=9
•Multiplication8*x=32
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Commutative PropertyIf the order of the addends or factors is
changed, the sum or product stays the same.
•Addition4+9=9+4
•Multiplication2x8=8x2
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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)
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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
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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)
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Zero Property of MultiplicationThe product of any number and zero is zero.
•Multiplication12x0=0
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by D. Fisher
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(2 + 1) + 4 = 2 + (1 + 4)
Associative Property Associative Property of Additionof Addition
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3 + 7 = 7 + 3
Commutative Commutative Property of AdditionProperty of Addition
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8 + 0 = 8
Identity Property of Identity Property of AdditionAddition
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6 • 4 = 4 • 6
Commutative Property Commutative Property of Multiplicationof Multiplication
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17 + (-17) = 0
Inverse Property of Inverse Property of AdditionAddition
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2(5) = 5(2)
Commutative Property Commutative Property of Multiplicationof Multiplication
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3(2 + 5) = 3•2 + 3•5
Distributive PropertyDistributive Property
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6(7•8) = (6•7)8
Associative Property of Associative Property of MultiplicationMultiplication
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5 • 1 = 5
Identity Property of Identity Property of MultiplicationMultiplication
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(6 – 3)4 = 6•4 – 3•4
Distributive PropertyDistributive Property
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1(-9) = -9
Identity Property of Identity Property of MultiplicationMultiplication
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3 + (-3) = 0
Inverse Property of Inverse Property of AdditionAddition
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1 + [-9 + 3]
= [1 + (-9)] + 3Associative Property of Associative Property of
AdditionAddition
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-3(6) = 6(-3)
Commutative Property Commutative Property of Multiplicationof Multiplication
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-8 + 0 = -8
Identity Property of Identity Property of AdditionAddition
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3•7 – 3•4 = 3(7 – 4)
Distributive PropertyDistributive Property
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6 + [(3 + (-2)]
= (6 + 3) + (- 2)Associative Property Associative Property
of Additionof Addition
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7 + (-5) = -5 + 7
Commutative Commutative Property of AdditionProperty of Addition
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(5 + 4)9 = 45 + 36
Distributive PropertyDistributive Property
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-3(5 • 4) = (-3 • 5)4
Associative Property of Associative Property of MultiplicationMultiplication
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-8(4) = 4(-8)
Commutative Property Commutative Property of Multiplicationof Multiplication
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6(3 – 2n) = 18 – 12n
Distributive PropertyDistributive Property
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2x + 3 = 3 + 2x
Commutative Property Commutative Property of Additionof Addition
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ab = ba
Commutative Property Commutative Property of Multiplicationof Multiplication
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a + 0 = a
Identity Property of Identity Property of AdditionAddition
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a(bc) = (ab)c
Associative Property of Associative Property of MultiplicationMultiplication
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a•1 = a
Identity Property of Identity Property of MultiplicationMultiplication
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a +b = b + a
Commutative Property Commutative Property of Additionof Addition
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a(b + c) = ab + ac
Distributive PropertyDistributive Property
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a + (b + c) = (a +b) + c
Associative Property of Associative Property of AdditionAddition
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a + (-a) = 0
Inverse Property of Inverse Property of AdditionAddition