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Commutative Property of Addition
a + b = b + a

Commutative Property of Multiplication
ab = ba

Associative Property of Addition
changing the grouping of terms will not change the sum: a + b + c = (a + b) + c = a + (b + c)

Associative Property of Multiplication
changing the grouping of factors will not change the product: abc = (ab)c = a(bc)

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

Distributive Property of Subtraction
a(b-c) = ab - ac

Identity Property for Addition
The sum of zero and any number is that number.
0 + a = a

Identity Property of Multiplication
the product of any number and 1 is equal to the that number: a x 1 = a

Additive Inverse
a number & its opposite = 0:
a + (-a) = 0

Multiplicative Inverse
a(1/a) = 1

closure Property
A set is closed under an operation if and only if the operation on two elements of the set produces another element in the set. If an element outside the set is produced, then the operation is not closed.

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