Properties of Whole Numbers

Properties of Whole Numbers A whole number added to 0 remains unchanged.

A whole number added to 0 remains unchanged. Thus, 0 is called the additive identity in whole numbers.  The product of two whole numbers is the same, no matter in which order they are multiplied. This is called the commutative property of multiplication.  A whole number multiplied by 1 remains unchanged. Thus, 1 is called the multiplicative identity in whole numbers.  Whole numbers are closed under addition and multiplication.  Subtraction and division are not commutative in whole numbers. Whole numbers are not closed under subtraction and division.  While adding whole numbers, we can group the numbers in any order. This is called the associative property of addition.  While multiplying whole numbers, we can group them in any order. This is called the associative property of multiplication.  The sum of the products of a whole number with two other whole numbers is equal to the product of the whole number with the sum of the two other whole numbers. This is called the distributive property of multiplication over addition.