# Rational number The rational numbers (ℚ) are included in the real numbers (ℝ), and in turn include the integers (ℤ), which include the natural numbers (ℕ)

A rational number is any number that can be expressed as the quotient or fraction ${\frac {p}{q}}$ of two integers, a numerator p and a non-zero denominator q.

## Examples

1. ${\frac {1}{2}}$ 2. 5
3. 0.2

Notice the number 5 in second example! It is because all numbers are divisible by 1 and at such it is actually ${\frac {5}{1}}$ but it is more convenient to write it as 5. Note Though all numbers are divisible by 1 some numbers are considered irrational ie they cannot be represented in the form ${\frac {a}{b}}$ also note that it impossible to have a number with 0 as the denominator (b must not be equal to 0 in ${\frac {a}{b}}$ ).

## Operations Involving Rational Numbers

${\frac {a}{b}}$ + ${\frac {c}{d}}$ = ${\frac {ad+bc}{cd}}$ ### Subtraction

${\frac {a}{b}}$ - ${\frac {c}{d}}$ = ${\frac {ad-bc}{cd}}$ ### Multiplication

${\frac {a}{b}}$ ${\frac {c}{d}}$ = ${\frac {ac}{bd}}$ ### Division

${\frac {a}{b}}$ ÷ ${\frac {c}{d}}$ = ${\frac {a}{b}}$ ${\frac {d}{c}}$ = ${\frac {ad}{bc}}$ .