# Rational number definition explained

Learn the rational number definition and also know the examples of rational number. Learning the definitions is very much important for students. In rational numbers we have positive and negative rational numbers that also we will study now. We know in mathematics we have so many types of numbers. In that rational number is also one of the types of numbers. The order of the numbers if we take it follow like this ….natural numbers(N), whole numbers(W), integers(I) and rational numbers(Q). I hope that up to integers you know the definitions of numbers so now we will learn the definition of rational numbers.

## what is rational number definition?

If the number is expressed in the form of $\frac { x }{ y }$ where x and y are integers and y ≠ 0 then it is called as a rational number. The symbol for representing rational number is the letter “Q”.

Examples:

$\frac { 1 }{ 8 }$, $\frac { 5 }{ 9 }$, $\frac { -4 }{ 3 }$, $\frac { -17 }{ -12 }$, 5, -9, 0, ……………..

Note:

Smallest rational number – does not exist.

Greatest rational number – does not exist.

### Positive rational number definition:

In the given rational number if both numerator and denominator have same sign then it is called as positive rational number.

Examples:

$\frac { -7 }{ -9 }$, $\frac { -15 }{ -69 }$, $\frac { 18 }{ 73 }$, $\frac { 61 }{ 29 }$,…………….

#### Negative rational number definition:

Suppose in the given rational number if numerator and denominator has opposite sign then it is called as negative rational number.

Example:

$\frac { -45 }{ 65 }$, $\frac { -19 }{ 34 }$, $\frac { 85 }{ -47 }$, $\frac { 99 }{ -52 }$,…………….

Note:

All natural numbers, whole numbers and integers are rational numbers but vice versa is not correct always. 