Rational numbers/Advanced Study

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

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

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

See Also

• Portal: Mathematics
• Wikipedia: Rational number
• MathsIsFun: Rational Numbers