Properties of numbers

While counting any quantity we use numbers 1,2,3….and so on. In various calculations using numbers the four basic operations used are the addition, subtraction, multiplication and division. Based on these operations there are properties of numbers which make the calculations simpler. These properties lay the foundation to work with different equations and hence it is important to get familiar with them. To the question What are the Properties of Numbers, we can say that the basic property number are the commutative property, associative property, distributive property and Identity.

Commutative Property: A given operation is said to be commutative if when the numbers are interchanged the value of the result remains the same. When numbers are added in whatever order the result remains unchanged and hence addition operation is commutative.

For Example:  3+4=7 also 4+3=7.
When numbers are multiplied in any order the result remains unchanged and hence the multiplication operation is commutative.

For Example: 3x7=21 also 7x3=21. Subtraction operation and division operation are not commutative as the result changes when numbers are interchanged; 7-4=3 but 4-7 = -3; 12/3=4 but 3/12=1/4, here the results are different when numbers are interchanged.

Associative Property: A given operation is said to be associative if when the change in the grouping does not change the result.
When numbers are added the grouping of numbers does not change the result and hence addition operation is associative. For example: 3+(4+5) is same as (3+4)+5. When numbers are multiplied the grouping of numbers does not change the result and hence multiplication operation is associative. For example: 2x(4x5) is same as (2x4)x5.
Subtraction operation and Division operation are not associative.

Distributive Property: This property helps to multiply the number outside with each of the terms inside the parenthesis thus helps to remove the parenthesis. For example: 3(a+b)= 3.a + 3.b= 3a+3b; (x-2)(y+3) each of the terms in the first parenthesis is multiplied with each of the terms in the second parenthesis giving the required product, xy+3x-2y-6.

Identity Property: When a zero is added to any number the result is the same number and hence zero is called the additive identity. For example: 3+0=3. When a number is multiplied by one the result is always the same number and hence one is multiplicative identity. For example: 4x1=4

The other property of numbers is multiplicative inverse, the product of any number and its inverse is always one, a x 1/a=1; 1/a is the multiplicative inverse of a. Zero property, when any number is multiplied with zero the product is zero, ax0=0