Rational numbers/Advanced Study



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
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 $$\frac a b$$).
 * 1) $$\frac {1} {2}$$
 * 5
 * 1) 0.2

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