Class5.Operations on Rational Numbers| 7th | mathematics|

        5.Operations on Rational Numbers

Natural numbers:
The groups of the positive numbers which are countable are known as natural numbers. The examples of natural numbers will be 1, 2, 3, 4, 5, etc.
On solving equations like x + 3 = 12, we get the solution as x = 9. The solution 9 is a natural number.

Whole numbers:
The groups of natural numbers with inclusion of zero in it are known as whole numbers. The examples of whole numbers will be 0, 1, 2, 3, 4, 5, etc.
On solving equations like x + 7 = 7, we get the solution as x = 0. The solution 0 is a whole number.
For the given equation, if we would have considered only the natural numbers, then we could not have found the solution. By adding zero to group of natural numbers we get the whole numbers.

Integers:
The groups of positive and negative numbers along with zero are known as integer numbers. The examples of integer numbers will be -3, -2, -1, 0, 1, 2, 3, 4, 5, etc.
On solving equations like x + 12 = 7, we get the solution as x = -5. The solution -5 is an integer.
For the given equation, if we would have considered only the whole numbers, then we could not have found the solution. By adding negative numbers to group of whole numbers we get the integer numbers.

Rational numbers:
The numbers which can be expressed as ratio of integers are known as rational numbers. The examples of rational numbers will be 1/4, 2/7, - 3/10, 34/7, etc.
On solving equations like 3x + 5 = 0, we get the solution as x = -5/3. The solution -5/3 is neither a natural number or whole number or integer.
This leads us to the collection of Rational Numbers. These are the numbers which can be expressed in x/y form; where y ≠ 0.

Properties of Rational Numbers:
(i) Closure Property:
When any operation is performed between two or more rational numbers and their result is also a rational number then we say that the rational numbers follow the closure property for that op

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