# Fundamental Mathematics/Arithmetic/Arithmetic Number/Fraction

(Redirected from Fraction)

## Fraction

Fraction can be understood as ratio of Numerator over Denomator

${\displaystyle {\frac {A}{B}}={\frac {Numerator}{Denominator}}}$

## Mixed Fraction

Examine a fraction that has numerator less than denominator

${\displaystyle {\frac {3}{4}}=0.75}$ This represents a fraction of a whole number

A fraction that has numerator is equal denominator

${\displaystyle {\frac {4}{4}}=1}$ .This represents a whole number

${\displaystyle {\frac {3}{4}}+{\frac {4}{4}}={\frac {7}{4}}}$

Yields a fraction that has numerator greater than denominator

Which can be written as

${\displaystyle 1{\frac {3}{4}}}$

This type of fraction is called Mixed fraction

## Improper Fractions

This is a type of fraction where the numerator is larger or bigger than the denominator in ${\displaystyle {\frac {A}{B}}}$ such that A > B examine the following:

${\displaystyle {\frac {23}{2}}}$

23 is larger than 2.

${\displaystyle {\frac {9}{4}}}$

9 is larger than 4.

All of the above are called improper fractions.

## Equal Fractions

Given 2 fractions ${\displaystyle {\frac {A}{B}}}$ and ${\displaystyle {\frac {C}{D}}}$ . 2 fractions are equal if

${\displaystyle A=C,B=D}$

## Mathematic Operation

### Operation on 1 fraction

${\displaystyle ({\frac {A}{B}})^{0}=1}$
${\displaystyle ({\frac {A}{B}})^{1}={\frac {A}{B}}}$
${\displaystyle ({\frac {A}{B}})^{-1}={\frac {1}{\frac {A}{B}}}={\frac {B}{A}}}$
${\displaystyle ({\frac {A}{B}})^{n}={\frac {A^{n}}{B^{n}}}}$

### Operation on 2 different fractions

 Addition ${\displaystyle {\frac {A}{B}}+{\frac {C}{D}}={\frac {AD+BC}{BD}}}$ ${\displaystyle {\frac {2}{3}}+{\frac {5}{2}}={\frac {(2\times 2)+(3\times 5)}{3\times 2}}={\frac {4+15}{6}}={\frac {19}{6}}=3{\frac {1}{6}}}$ Subtraction ${\displaystyle {\frac {A}{B}}-{\frac {C}{D}}={\frac {AD-BC}{BD}}}$ ${\displaystyle {\frac {2}{3}}-{\frac {5}{2}}={\frac {(2\times 2)-(3\times 5)}{3\times 2}}={\frac {4-15}{6}}={\frac {-11}{6}}=-1{\frac {5}{6}}}$ Multiplication ${\displaystyle {\frac {A}{B}}\times {\frac {C}{D}}={\frac {AC}{BD}}}$ ${\displaystyle {\frac {2}{3}}\times {\frac {5}{2}}={\frac {2\times 5}{3\times 2}}={\frac {10}{6}}={\frac {5}{3}}=1{\frac {2}{3}}}$ Division ${\displaystyle {\frac {A}{B}}}$ ÷ ${\displaystyle {\frac {C}{D}}}$ = ${\displaystyle {\frac {A}{B}}{\frac {D}{C}}={\frac {A}{B}}\times {\frac {D}{C}}={\frac {AD}{BC}}}$ ${\displaystyle {\frac {\frac {2}{3}}{\frac {5}{2}}}={\frac {2}{3}}\times {\frac {2}{5}}={\frac {4}{15}}}$