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a+b = b+a
 Commutative Property of Addition
 the order in which two whole numbers are added does not change their sum.

a x b = b x a
 Commutative Property of Multiplication
 the order in which two whole numbers are multiplied does not change their product.

(a+b) + c = a + (b+c)
 Associative Property of Addition
 when the grouping of addends is changed, the sum is the same.

(a x b) x c = a x (b x c)
 Associative Property of Multiplication
 the way factors are grouped does not change the product.

a + 0 = a and 0 + a = a
 The Addition Property of Zero
 The sum of any whole number and 0 is the same whole number. 0 is called the "identity element for addition".

a x 1 = a and 1 x a = a
 Multiplication Property of One
 the product of any whole number and 1 is the same whole number.
 1 is the identity element for multiplication.

a x 0 = 0 and 0 x a = 0
 Multiplication Property of Zero
 the product of any whole number and 0 is 0.

a  0 = a and a  a = 0
 Subtraction Property of 0
 The difference of any whole number and 0 is the same whole number. AND the difference of any whole number and itself is 0.

 Division Property of One
 A whole number divided by 1 will always result in the quotient being the same whole number as the dividend. AND a whold number divided by itself will always result in 1.

For any whole number a, except 0:
0 ÷ a= 0
 Division Property of Zero:
 0 divided by any whole number will always result in 0.

a x (b + c) = (a x b) + (a x c)
and
(b + c) x a = (b x a) + (c x a)
 Distributive Property of Multiplication with Respect to Addition
 multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products.


a x (b – c) = (a x b) – (a x c)
and
(b – c) x a = (b x a) – (c x a)
 Distributitve Property of Multiplication with Respect to Subtraction
 multiplying a difference by a number is the same as multiplying each number from the subtraction problem by the factor and then subtracting the products.









