Fundamental Mathematics/Arithmetic/Arithmetic Number/Fraction

Fraction

Fraction can be understood as ratio of Numerator over Denomator

${\frac {A}{B}}={\frac {Numerator}{Denominator}}$ Mixed Fraction

Examine a fraction that has numerator less than denominator

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

A fraction that has numerator is equal denominator

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

${\frac {3}{4}}+{\frac {4}{4}}={\frac {7}{4}}$ Yields a fraction that has numerator greater than denominator

Which can be written as

$1{\frac {3}{4}}$ 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 ${\frac {A}{B}}$ such that A > B examine the following:

${\frac {23}{2}}$ 23 is larger than 2.

${\frac {9}{4}}$ 9 is larger than 4.

All of the above are called improper fractions.

Equal Fractions

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

$A=C,B=D$ Mathematic Operation

Operation on 1 fraction

$({\frac {A}{B}})^{0}=1$ $({\frac {A}{B}})^{1}={\frac {A}{B}}$ $({\frac {A}{B}})^{-1}={\frac {1}{\frac {A}{B}}}={\frac {B}{A}}$ $({\frac {A}{B}})^{n}={\frac {A^{n}}{B^{n}}}$ Operation on 2 different fractions

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