# Arithmetic/Types of Numbers/Fraction

## Fraction

Fraction is a ratio of two integer numbers. Fraction can be expressed mathematically

${\displaystyle {\frac {A}{B}}}$, where B is not zero.

Where

A is called Numerator
B is called Denominator

## Equal Fractions

Two fractions A/B and C/D are the same if the product of numerator A and denominator D is equal to the product of denominator B and numerator C.

${\displaystyle {\frac {A}{B}}={\frac {C}{D}}}$ if ${\displaystyle A*D=B*C}$
and

${\displaystyle {\frac {A*D}{B*C}}={\frac {E*H}{F*G}}}$ if ${\displaystyle (A*D)(G*F)=(E*H)(B*C)}$

## Rules

1. ${\displaystyle {\frac {A}{B}}}$ + ${\displaystyle {\frac {C}{D}}}$ = ${\displaystyle {\frac {AD+BC}{BD}}}$
2. ${\displaystyle {\frac {A}{B}}}$ - ${\displaystyle {\frac {C}{D}}}$ = ${\displaystyle {\frac {AD-BC}{BD}}}$
3. ${\displaystyle {\frac {A}{B}}}$ x ${\displaystyle {\frac {C}{D}}}$ = ${\displaystyle {\frac {AC}{BD}}}$
4. ${\displaystyle {\frac {A}{B}}}$ / ${\displaystyle {\frac {C}{D}}}$ = ${\displaystyle {\frac {AD}{BC}}}$, if C not zero.