This collection of LaTeX macros make it easier to insert fractions, including defining a \fracshort macro that causes a fraction to be rendered like $a/b$ (making it easier to switch between $\frac{a}{b}$ and $a/b$). The slash inserted by \fracshort scales with the height of the numerator and denominator. Also included are common fractions, $\frac{1}{2}$ (\half), $\frac{1}{3}$ (\third), etc. Each of these commands can take one optional argument that sets the numerator to the given values, such as \half[x] ($\frac{x}{2}$), and have short versions (\quartershort[\theta] creates $\theta/4$) and a display style version (e.g., \dtenth[n] creates $\dfrac{n}{10}$, but you should never use display style fractions in a line of text). Finally, the \oneover, \oneovershort, and \doneover macros inserts fractions with $1$ in the numerator and the denominator given as an argument: \oneover{x} creates $\frac{1}{x}$.

When using the short fractions, make sure you insert parentheses, as needed, around the numerator and denominator!

Definition 
\newcommand{\fracshort}[2]{\left.#1 \middle/ #2\right.}
\newcommand{\oneover}[1]{\frac{1}{#1}}
\newcommand{\doneover}[1]{\dfrac{1}{#1}} % \displaystyle fraction
\newcommand{\oneovershort}[1]{\fracshort{1}{#1}}
% Common Fractions
\newcommand{\half}   [1][1]{\frac{#1}{2}}
\newcommand{\third}  [1][1]{\frac{#1}{3}}
\newcommand{\quarter}[1][1]{\frac{#1}{4}}
\newcommand{\fifth}  [1][1]{\frac{#1}{5}}
\newcommand{\sixth}  [1][1]{\frac{#1}{6}}
\newcommand{\eighth} [1][1]{\frac{#1}{8}}
\newcommand{\tenth}  [1][1]{\frac{#1}{10}}
\newcommand{\twelfth}[1][1]{\frac{#1}{12}}
% Short fractions for inline equations.
\newcommand{\halfshort}   [1][1]{\fracshort{#1}{2}}
\newcommand{\thirdshort}  [1][1]{\fracshort{#1}{3}}
\newcommand{\quartershort}[1][1]{\fracshort{#1}{4}}
\newcommand{\fifthshort}  [1][1]{\fracshort{#1}{5}}
\newcommand{\sixthshort}  [1][1]{\fracshort{#1}{6}}
\newcommand{\eighthshort} [1][1]{\fracshort{#1}{8}}
\newcommand{\tenthshort}  [1][1]{\fracshort{#1}{10}}
\newcommand{\twelfthshort}[1][1]{\fracshort{#1}{12}}
% Display style fractions.
\newcommand{\dhalf}   [1][1]{\dfrac{#1}{2}}
\newcommand{\dthird}  [1][1]{\dfrac{#1}{3}}
\newcommand{\dquarter}[1][1]{\dfrac{#1}{4}}
\newcommand{\dfifth}  [1][1]{\dfrac{#1}{5}}
\newcommand{\dsixth}  [1][1]{\dfrac{#1}{6}}
\newcommand{\deighth} [1][1]{\dfrac{#1}{8}}
\newcommand{\dtenth}  [1][1]{\dfrac{#1}{10}}
\newcommand{\dtwelfth}[1][1]{\dfrac{#1}{12}}

Examples

Code Output 
\fracshort{a}{b}
 $$a/b $$ 
\fracshort{1}{\left(1 + e^{x^{-2}}\right)}
 $$\left. 1 \middle/ \left(1 + e^{x^{-2}}\right) \right. $$ 
\half
 $$\frac{1}{2} $$ 
\half[x]
 $$\frac{x}{2} $$ 
\third \fourth \fifth \sixth \twelfth
 $$\frac{1}{3}\frac{1}{4}\frac{1}{5}\frac{1}{6}\frac{1}{12} $$ 
\third[a] \fourth[b] \fifth[c] \sixth[d] \twelfth[e]
 $$\frac{a}{3}\frac{b}{4}\frac{c}{5}\frac{d}{6}\frac{e}{12} $$ 
\thirdshort[a] + \fourthshort[b]
$$a/3 + b/4 $$