Properties of Real Numbers

In this lesson, we will learn about properties of real numbers in detail so that it will be helpful for you to solve algebra problems.

Before going ahead , let’s revise what are the real numbers


The non-imaginary or non-complex numbers that include rational and iraational numbers are called real numbers

Real numbers properties are

1. Communitative Property

This property of real numbers say the order of addition or multiplication do not effect the result of addition or multiplication of real numbers.


3 +a =a +3 (communitative property w.r.t. addition)

3 *a =a* 3 (communitative property w.r.t. multiplication)

2. Associative Property

This property says for addition or multiplication of more than two numbers , we can have any order with no effect on the resulting value


( a + b ) + c= a + ( b + c ) ( associative property w.r.t. addition)

( a * b ) * c = a * ( b * c ) ( associative property w.r.t. multiplication)

3. Distributive Property

This property of real number deals with the situation involving both addition and multiplication at same time

2a (x + y ) = 2ax + 2ay

4. Density Property

This property says an endless list of numbers can be found between two real numbers.


Between 0.1 and 0.2 , we can find 0.11 , 0.12 , 0.13…..

5. Identity Property

This property says on adding 0 to any real number or multiplying 1 to any real number returns the same number. Hence , 0 and 1 are called additive identity or multiplicative identity respectively.


a + 0 = a

a * 1= a

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