# Amplifying fractions

I want to make myself a math portofolio (as a quick reference) and I have a part where I have to 'amplify' a fraction like here:

But I don't know how can I do this thing, can you help me? Thank you.

Edit: The "4)" in the upper left-hand corner means "amplify", the process of expanding both numerator and denominator by explicitly stating the value indicated as a multiplication factor. Similarly, a "(4" in the upper right-hand corner means "simplify", or merge the separate values in the numerator and denominator to a single value.

• And what exactly should amplify mean in this context? – daleif Jul 27 '15 at 8:45
• @daleif The thing in the left corner, because eh, this is how we romanians and a part of the world do it. – Stefan Alecu Jul 27 '15 at 8:50
• @StefanAlecu -- please explain "amplify" in the text of the question. i wasn't familiar with the term either until i read your response to daleif's question, although i was wondering what the "4)" meant. (all the answers so far have neglected that component, and concentrated only on the coloring.) – barbara beeton Jul 27 '15 at 8:56
• @StefanAlecu -- i've edited in an explanation of "amplify" and "simplify", so that these terms can be found in a search. (it's very hard to search on comments.) if the explanation isn't correct, please fix it. – barbara beeton Jul 27 '15 at 11:33

You should define a set of custom markup commands (see [1], [2]) for those fraction types, where you employ the xcolor package and the \prescript command from mathtools to do the needed formatting:

\documentclass{article}
\usepackage{mathtools,xcolor}

\newcommand{\coloredfrac}[3][red]{%
\frac{\color{#1}#2}{\color{#1}#3}
}

\newcommand{\ampfrac}[3]{%
\prescript{#1}{}{\frac{#2}{#3}}
}

\newcommand{\simpfrac}[3]{%
\frac{#2}{#3}^{#1}
}

\begin{document}
$\ampfrac{4)}{1}{2}=\coloredfrac{1\cdot 4}{2\cdot 4}=\simpfrac{(4}{4}{8}$
\end{document}


Regarding your request for a more sophisticated coloring macro that is able to color the numerator and the denominator indipendantly you could define:

\newcommand\coloredfrac{\kernel@ifnextchar[{\coloredfrac@}{\coloredfrac@[red]}}
\def\coloredfrac@[#1]{\kernel@ifnextchar[{\coloredfrac@@[#1]}{\coloredfrac@@[#1][#1]}}
\def\coloredfrac@@[#1][#2]#3#4{%
\frac{\color{#1}#3}{\color{#2}#4}
}


\coloredfrac can now be called

• without optional arguments to get a colored fraction in the default color, which is red in this example
• with one optional argument that sets the color for both, the numerator and the denominator
• with two optional arguments; the first one for the color of the numerator and the second one for the color of the denominator

\documentclass{article}
\usepackage{mathtools,xcolor}

\makeatletter
\newcommand\coloredfrac{\kernel@ifnextchar[{\coloredfrac@}{\coloredfrac@[red]}}% default value: red
\def\coloredfrac@[#1]{\kernel@ifnextchar[{\coloredfrac@@[#1]}{\coloredfrac@@[#1][#1]}}
\def\coloredfrac@@[#1][#2]#3#4{%
\frac{\color{#1}#3}{\color{#2}#4}
}
\makeatother

%\newcommand{\ampfrac}[3]{%
%  \prescript{#1}{}{\frac{#2}{#3}}
%}

%\newcommand{\simpfrac}[3]{%
%  \frac{#2}{#3}^{#1}
%}

\begin{document}
$\coloredfrac{1}{2}=\coloredfrac[green]{2}{4}=\coloredfrac[green][blue]{4}{8}$
\end{document}


• Finally, one answer that answered my question. Thank you. Does it work the other way, to have (4 in the right corner? (that is what we call simplifying) – Stefan Alecu Jul 27 '15 at 9:00
• Sure, with something like: \newcommand{\simpfrac}[3]{\frac{#2}{#3}^{#1}} – Ruben Jul 27 '15 at 9:05

Here is a solution

\documentclass{article}
\usepackage{xcolor}

\begin{document}

$\raisebox{\baselineskip}{4)}\frac{1}{2}=\frac{\textcolor{red}{1\cdot4}}{\textcolor{red}{2\cdot4}}=\frac{4}{8}$
$\raisebox{\baselineskip}{4)}\frac{1}{2}=\frac{\textcolor{red}{1\cdot4}}{\textcolor{red}{2\cdot4}}=\frac{4}{8}$

\end{document}


• It's good, but there is a problem. I want to display the thing in the left corner, the 4). That is what I don't know how to do. – Stefan Alecu Jul 27 '15 at 8:52
• while this takes care of the fractions, it doesn't cover the "4)" in the upper left corner. (see comments on the question. i didn't know what "amplify" meant either, until i read those.) – barbara beeton Jul 27 '15 at 8:53
• I guess it was also my fault that I didn't specify. – Stefan Alecu Jul 27 '15 at 8:57
• @StefanAlecu answer edited – touhami Jul 27 '15 at 8:58

Do you perhaps mean something like "highlight" by "amplify"?

Anyway, I think

\newcommand{\colorfrac}[3][red]{\frac{{\color{#1} #2}}{{\color{#1} #3}}}


\colorfrac{1}{2}


would give a red '1/2' and

\colorfrac[green]{1}{3}


a green one (needs the color package).

## Edit

As an answer to your comment: Of course you could, manually using \frac{{\color{color1} 1}}{{\color{color2} 2}} or by a command similar to the one defined above.

Okay, now I understood what you want. One solution (\prescribe in the other one is probably better, but still):

\newcommand{\amplfrac}[3]{\frac{\llap{$^{(#1)}$}#2}{#3}}

• Nope, but at least now I know how to color fractions. Can you color individual parts of a fractions (the top only)? – Stefan Alecu Jul 27 '15 at 8:52
• edited my answer – Bort Jul 27 '15 at 9:02
• I think for the individual coloring it is best to have a syntax with optional arguments, like \colorfrac[<color-num>][<color-den>]{<num>}{<den>} -- and \colorfrac[<color-both>]{<num>}{<den>} should be available too (see my answer). – Ruben Jul 27 '15 at 11:43