Properties of Integers

The property which states that changing the order of the addends does not affect the sum.

a + b = b + a

• Commutative Property of Addition

• Commutative Property of Multiplication

• Associative Property of Addition

It states that changing the groupings of the addends does not affect the sum:

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

• Commutative Property of Multiplication

• Associative Property of Addition

• Associative Property of Multiplication

A property which states that the sum of the integers a and b is an integer.

• Closure Property

• Zero Property

• Distributive Property

It states that changing the groupings of the factors does not affect the product:

a x ( b x c ) = ( a x b ) x c

• Commutative Property of Multiplication

• Commutative Property of Addition

• Associative Property of Multiplication

This property states that any number added by 0 is equal to the number:

a + 0 = a

• Identity Property of Addition

• Identity Property of Multiplication

• Zero Property

It states that any number multiplied by 1 is equal to the number:

a x 1 = a

• Identity Property of Addition

• Identity Property of Multiplication

• Zero Property

The property which states that changing the order of the factors does not affect the product:

a x b = b x a

• Commutative Property of Addition

• Commutative Property of Multiplication

• Associative Property of Addition

This states that any number multiplied by zero is equal to 0:

a x 0 = 0

• Identity Property of Addition

• Identity Property of Multiplication

• Zero Property

This property states that adding first before multiplying or distributing the factor to each addend will give same answer:

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

• Distributive Property

• Commutative Property

• Associative Property of Addition

It states that the sum of a number and its opposite is 0.

• Zero Property

• Multiplicative Inverse Property

• Additive Inverse property