How to present a vertical multiplication/addition

Question

How do I present vertical (columnar) multiplication and addition in LaTeX. Like this: http://mathworld.wolfram.com/LongMultiplication.html

    3 8 4
x     5 6
---------
  2 3 0 4
1 9 2 0
---------
2 1 5 0 4

I used the "array" environment. But i have right align problem. Any other best ideas?

Answer 1

the xlop package does this sort of thing. It does warn that it uses "french conventions", but at least for multiplication it looks fine, to me.

disclaimer: i last did multiplication sums in school in the 1950s...

\documentclass{article}
\usepackage{xlop}
\begin{document}
\opmul{384}{56}\qquad
\end{document}

Answer 2

How about a simple tabular environment:

\documentclass{article}
\begin{document}
\begin{tabular}{cccc}
  & 1 & 2 & 3 \\
+ &   & 3 & 4 \\
\hline
  & 1 & 5 & 7 \\
\end{tabular}
\end{document}

If you need to change spacing, you can use the @ specifier which automatically puts arguments in braces as a space between columns (in this case a thin space \,).

\documentclass{article}
\begin{document}
\begin{tabular}{c@{\,}c@{\,}c@{\,}c}
  & 1 & 2 & 3 \\
+ &   & 3 & 4 \\
\hline
  & 1 & 5 & 7 \\
\end{tabular}
\end{document}

Some other spaces are a thick space \; and a medium space \:. It is also possible to avoid the onerous typing of repeating column types by using the *{}{}:

\begin{tabular}{c*{3}{@{\,}c}}

That produces c, and then 3 times @{\,}c, which combines to c@{\,}c@{\,}c@{\,}c.

Answer 3

I think the simplest (least complicated) solution is to use \phantom, as follows:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}\begin{array}{c}
\phantom{\times99}384\\
\underline{\times\phantom{999}56}\\
\phantom{\times9}2304\\
\underline{\phantom\times1920\phantom9}\\
\phantom\times21504
\end{array}\end{equation*}
\end{document}

Here, amsmath is needed for the equation* environment only; if you used equation you'd need no \usepackage at all. array allows multiple-line equations; \\ starts a new line. And \phantom{foo} prints a space the width of the characters foo. I've usually found 9 to be a good stand-in for any digit, but (e.g. if you have a few 1s) you may need to fiddle with it a bit.

Answer 4

Here is one way using Plain-commands:

\vbox{
  \openup2pt
  \def\trule{\noalign{\smallskip\hrule\smallskip}}
  \halign{&\tabskip1em$\mathstrut#$\cr
          &   & 3 & 8 & 4 \cr
    \times&   &   & 5 & 6 \cr
    \trule
          & 2 & 3 & 0 & 4 \cr
    1     & 9 & 2 & 0 \cr
    \trule
    2     & 1 & 5 & 0 & 4 \cr
  }
}
\bye

Answer 5

It is always preferable for a problem like this to let TeX do the calculations for you. Here is a draft solution and it does not use any tables. It still misses a small iteration macro to be completed, but I decided to post it, as it is easier to understand the code at this stage of development.

\documentclass{article}
\usepackage{fp,intcalc}
\begin{document}
  \def\multiplication#1#2{
  \def\answer{\FPmul\temp{#1}{#2}
   \parindent=0pt
   \FPround\temp{\temp}{0}\temp}
   \def\linea{#1}
   \def\lineb{$\times$\hfill#2}
   \def\linez##1##2##3{
   \intcalcMul{#1}{##2}##3}
   \def\Rule{\rule{1.5cm}{0.4pt}}
   \begin{minipage}[t]{1.5cm}
     \begin{flushright}
       \linea\\
       \lineb\\[-2pt]
       \Rule\\
       \def\Z{\phantom{0}}
       \linez{#1}{3}{}\\
       \linez{#1}{2}{\Z}\\[-8pt]
       \Rule
       \answer
     \end{flushright}
   \end{minipage}}
\multiplication{35670}{23}
\end{document}    

I have used both the fp package as well as the intCalc package to perform the calculations for demonstration purposes. It will be preferable to perform these calculations with the fp package in order to handle decimals correctly. One possibility also is to use a random function to set the what I presume are exercises randomly as well as produce the answers.

In many European countries the x operator would be typeset on the right.

Answer 6

Simply use any array environment \begin{array} or \beign{align} or the most powerfull tool \begin{IEEEeqnarray} and put a \cline[i-j] in it where i & j are the coloumns numbers

\begin{IEEEeqnarray*}{crCl}
        & 4 &\equiv& (1, 0, 4)\\
    +& 9 &\equiv& (0, 1, 4)\\[-7pt]
     \cline{1-4} 
    & 13 &\equiv& (1, 1, 3)
\end{IEEEeqnarray*}

produces the following