# Tweaking a Multiplication Table

• MHB
• topsquark
In summary, the conversation discusses ways to improve the formatting of multiplication tables on a forum. Suggestions include removing certain lines and using MathJAX or TikZ to create the tables. The final suggestions involve using a matrix of math nodes in TikZ to create the desired table format.
topsquark
Gold Member
MHB
I recently posted a couple of multiplication tables and I feel it needs a tweak:

$$\displaystyle \begin{array}{c||c|c|c|c|} V & e & a & b & c \\ \hline \hline e & e & a & b & c \\ a & a & e & c & b \\ b & b & c & e & a \\ c & c & b & a & e \end{array}$$

The LaTeX on the forum doesn't like the double lines || or = (as lines, not the equal sign!). Does anyone know how to make the lines bold faced or something? I feel the top line and first vertical line should be singled out in some way.

-Dan

Hey Dan,

There are some suggestions in https://mathhelpboards.com/tikz-pictures-63/4-element-4-element-multiplication-table-21434.html.
In particular a MathJAX suggestion and a TikZ suggestion.

To summarize:
Opalg said:
One way is to keep only those two lines and remove all the others: $$\begin{array}{c|cccc} + & a&b&c&d \\ \hline a&a&b&c&d\\ b&b&a&d&c \\ c&c&d&a&b \\ d&d&c&b&a \end{array}.$$

I like Serena said:
My previous TikZ suggestion had the 'problem' that math symbols had to have \\$ symbols around them.
Turns out there is a better way by using a [M]matrix of math nodes[/M] instead of a [M]matrix of nodes[/M].
Then all nodes are already in math mode.
Other than that the solution is the same.
\begin{tikzpicture}
\usetikzlibrary{matrix}

\matrix (m) [nodes={minimum width=3em,minimum height=3ex},matrix of math nodes]
{
\times & 0 & 1 & \theta & \theta + 1 \\
0 & 0 & 0 & 0 & 0\\
1 & 0 & 1 & \theta & \theta + 1\\
\theta & 0 & \theta & \theta + 1 & 1 \\
\theta + 1 & 0 & \theta + 1 & 1 & \theta \\
};

\draw[very thick] (m-1-1.north east) -- (m-5-1.south east);
\draw[very thick] (m-1-1.south west) -- (m-1-5.south east);
\foreach \x in {2,...,5}{
\draw (m-1-\x.north east) -- (m-5-\x.south east);
\draw (m-\x-1.south west) -- (m-\x-5.south east);
}
\end{tikzpicture}
[latexs]\begin{tikzpicture}
\usetikzlibrary{matrix}

\matrix (m) [nodes={minimum width=3em,minimum height=3ex},matrix of math nodes]
{
\times & 0 & 1 & \theta & \theta + 1 \\
0 & 0 & 0 & 0 & 0\\
1 & 0 & 1 & \theta & \theta + 1\\
\theta & 0 & \theta & \theta + 1 & 1 \\
\theta + 1 & 0 & \theta + 1 & 1 & \theta \\
};

\draw[very thick] (m-1-1.north east) -- (m-5-1.south east);
\draw[very thick] (m-1-1.south west) -- (m-1-5.south east);
\foreach \x in {2,...,5}{
\draw (m-1-\x.north east) -- (m-5-\x.south east);
\draw (m-\x-1.south west) -- (m-\x-5.south east);
}
\end{tikzpicture}[/latexs]

## 1. How do you "tweak" a multiplication table?

There are several ways to tweak a multiplication table. Some common methods include changing the order of the rows and columns, adding or subtracting a constant to each number, and multiplying or dividing each number by a constant.

## 2. What is the purpose of tweaking a multiplication table?

Tweaking a multiplication table can help students better understand the relationship between numbers and how multiplication works. It can also make the table more visually appealing and easier to memorize.

## 3. Can tweaking a multiplication table affect the accuracy of the results?

Yes, depending on the type of tweak applied, it can affect the accuracy of the results. For example, if a constant is added or subtracted to each number, the results will be slightly different from the original table.

## 4. Is there a specific order in which to apply tweaks to a multiplication table?

No, there is no specific order. However, it is important to keep track of the tweaks applied in order to accurately interpret the results.

## 5. Are there any other benefits to tweaking a multiplication table?

Aside from helping with understanding and memorization, tweaking a multiplication table can also be a fun and creative way to practice math skills. It can also be used to challenge students to find patterns and make predictions about the results.

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