Rational means anything which is completely logical whereas irrational means anything which is unpredictable and illogical in nature. The word rational has evolved from the word ratio . In general, rational numbers are those numbers that can be expressed in the form of , in which both p and q are integers and q≠0.We can denote these numbers by **Q.**

__Properties of rational numbers__

**Closure property:** For two rational numbers say x and y the results of addition, subtraction and multiplication operations gives a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example:

**Do you know why division is not under closure property?**

Division is not under closure property because division by zero is not defined. We can also say that except ‘0’ all numbers are closed under division. For example:

Division is not under closure property because division by zero is not defined. We can also say that except ‘0’ all numbers are closed under division. For example:

**Commutative law: **For rational numbers, addition and multiplication are commutative.

Commutative law of addition: a+b = b+a

Commutative law of multiplication: a×b = b×a

For example:

Subtraction is not a commutative property i. e. a-b ≠ b-a. This can be understood clearly with the following example

whereas

Division is also not commutative i.e. a/b ≠ b/a as,

whereas,

**Associative law: **Rational numbers follow the associative property for addition and multiplication.

Suppose x, y and z are rational then for addition: x+(y+z)=(x+y)+z

For multiplication: x(yz)=(xy)z.

Some important properties that should be remembered are:

- 0 is an additive identity and 1 is a multiplicative identity for rational numbers.
- For a rational number

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