# Rational number

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

## 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

### Addition

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

### Subtraction

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

### Multiplication

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

### Division

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