Properties of Real Numbers

What is a Real Number?
You can define real number as any valid number, be it whole number or rational number or irrational number. For example: 1, 1.234, 1/8, π, √7 are real numbers.

Properties of Real Numbers
There are certain properties that can be applied to all the real numbers. The different properties of real numbers are:

Cumulative Property
• Cumulative Property of Addition: This property of real numbers states that if there are two numbers, they can be added in any order. For example, 10 + 5 = 5 + 10

• Cumulative Property of Multiplication: This property states that the numbers can be multiplied in any order. For example, 10 X 5 = 5 X 10, both return the same value.

Associative Property
• Associative Property of Addition: If more numbers have to be added together, then you can associate any of them together in any way. For example, 10 + (5 + 2) = (10 + 5) + 2.

• Associative Property of Multiplication: If more numbers have to be multiplied together, then they can be associated in any way. For example, 10 X (5 X 2) = (10 X 5) X2.

Identity Property
• Identity Property of Addition: Any number added to zero will result in the number itself.  For example, 10 + 0 = 10.

• Identity Property of Multiplication: Any number added to one will result in the number itself. For example, 10 X 1 = 10.

Inverse Property
• Inverse Property of Addition: A positive number when added to its inverse results in zero. For example, 10 + (-10) = 0.

• Inverse Property of Multiplication: A number when multiplied by (1/same number) will result in 1. For example, 10 X (1 / 10) = 1.

Zero Property
Any number multiplied with zero results in zero. For example, 10 X 0 = 0

Density Property
 As per density property, it is always feasible to find a number existing between two real numbers. For example, between 10.1 and 10.2 you have a lot of numbers like 10.11, 10.12, and 10.13 and so on.

Distributive Property
Distributive property is applied when an expression includes addition and also multiplication. If a number is multiplied with a result of addition, then the multiplication has to be distributed over all the numbers participating in addition. For example, 2 X (5 + 10) = (2 X 5) + (2 X 10)

If you understand these properties clearly, then you can easily solve the algebra problems that include even complex expressions.