Showing posts with label Properties of Real Numbers. Show all posts
Showing posts with label Properties of Real Numbers. Show all posts

Tuesday, June 19, 2012

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.