## 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

You can also practice Algebra Equations.

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