Fundamental Mathematics/Arithmetic/Arithmetic Number/Fraction

Fraction[edit | edit source]

Fraction can be understood as ratio of Numerator over Denomator

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

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

Add 2 fractions above

{\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

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.

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

A=C,B=D

({\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}}}

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	${\frac {A}{B}}$ ÷ ${\frac {C}{D}}$ = ${\frac {A}{B}}{\frac {D}{C}}={\frac {A}{B}}\times {\frac {D}{C}}={\frac {AD}{BC}}$	${\frac {\frac {2}{3}}{\frac {5}{2}}}={\frac {2}{3}}\times {\frac {2}{5}}={\frac {4}{15}}$