# Basic Properties of Numbers in Mathematics

## Basic Properties of Numbers in Mathematics

There are four following basic properties of numbers in Mathematics:
1. Commutative
2. Associative
3. Distributive
4. Identity

It is especially important to understand these properties once we reach advanced mathematics such as Algebra & Calculus. Since, we should be familiar with each of these.

## 1. Commutative Property:

a. Addition: When two numbers are added, the sum is the same regardless of the order in which the numbers are added.
p+q=c or, q+p=c
For example:
3+4=7 or, 4+3=7

b. Multiplication: When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.
p x q = c or, q x p = c
For example:
3 x 4 = 12 or, 4 x 3 = 12

## 2. Associative Property:

a. Addition: When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.
p + (q + r) = c or, (p + q) + r = c
For example:
5 + (7 + 2) = 14 or, (5 + 7) + 2 = 14

b. Multiplication: When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.
p x (q x r) = c or, (p x q) x r = c
For example:
5 x (7 x 2) = 70 or, (5 x 7) x 2 = 70

## 3.Distributive Property:

The sum of two numbers times a third number is equal to the sum of each addend times the third number.
p x (q + r) = c or, p x q + p x r = c
For example:
3 x (5 + 6) = 33 or, 3 x 5 + 3 x 6 = 33

## 4. Identity Property:

a. Addition: The sum of any number and zero is that number.
p+0=p or, 0+p=p
For example:
3 + 0 = 3 or, 0+3=3

b. Multiplication: The product of any number and one is that number.
p x 1 = p or, 1 x p = p
For example:
6 x 1 = 6 or, 1 x 6 = 6

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