How can I make nice looking mathematical symbols, like fractions and radicals, on the OpenLab? This is not hard — but it takes a little getting used to.

Here’s an example. If you type this:

Here is a square root:  \begin{math} \sqrt{x+1} \end{math}

then, after you click the Submit button, you will see this:

Here is a square root:  

TIP: You can also use the “Preview” button to get a quick look at the results without Submitting them.

Each bit of mathematics begins with \begin{math} and ends with \end{math}.  In between, you type your math — many mathematical things can be typed just as they are, like numbers and variables, but for each special math symbol we use a code. Here are examples of codes for some of the most common symbols.

Basic examples: radicals, exponents, fractions

Radicals

In the example above, we use the code for the radical sign, which is \sqrt{ }. The stuff under the radical goes inside the curly braces { }.

If you type this:	You will see this:
\begin{math} \sqrt{x} \end{math}

Exponents

To make an exponent, use ^ (just like in your graphing calculator).

If you type this:	You will see this:
\begin{math} x^3 \end{math}

If your exponent contains more than a single letter or digit, you should group the exponent together using curly braces:

If you type this:	You will see this:
\begin{math} x^{5y} \end{math}

Fractions

The code for fractions is \frac{ }{ }, with the numerator inside the first set of curly braces { } and the denominator in the second set.

If you type this:	You will see this:
\begin{math} \frac{3}{5} \end{math}

Here is an example with more complicated numerator and denominator:

If you type this:	You will see this:
\begin{math} \frac{x^3 y^5 z}{x y^2} \end{math}

Advanced examples: large parentheses, higher roots

Large parentheses

In many cases you can just use regular parentheses ( ). BUT if you want your parentheses to get bigger, for example to wrap around an entire fraction, then you should use \left( and \right) instead. Here’s an example showing how we can raise an entire fraction to a power:

If you type this:	You will see this:
\begin{math} \left( \frac{2x}{5} \right)^4 \end{math}

Higher roots

Regular radical signs use the \sqrt{} command. For higher roots (cube roots, fourth roots, and so on) we use \sqrt[n]{ }, where n is the index of the root (in this example, n is 5).

If you type this:	You will see this:
\begin{math} \sqrt[5]{32xy} \end{math}

Hints and suggestions

Preview your work. If you are typing a response in one of the boxes on this site, you can use the “Preview” button (just above the box) to get a sense of what your response will look like when you Submit it. It will convert all of your math codes into symbols, and will tell you if there are any errors. To continue typing, click the “Edit” button.

Don’t start with a complicated formula. Write a short bit of math, and use the Preview button to see what it looks like. Then make corrections until it looks just the way you want.

Stuck? Frustrated? Doesn’t look the way you want it to look? Feel free to include questions about typing math right here on this site – we’ll do our best to answer them. Let us know what you’ve tried so far, and what you’re trying to accomplish.

For more examples, this link is a pretty good place to start. Want even more symbols? Here you go.

Quick reference and sample questions

	Type this:	to get this result:
Basic fractions:	\begin{math} \frac{2}{7} \end{math}
More complicated fractions:	\begin{math} \frac{x+1}{x^2 + 5x} \end{math}
Complex fractions:	\begin{math} \frac{2x+7}{x^2+\frac{x}{2}} \end{math}
Basic exponents:	\begin{math} x^3 \end{math}
	\begin{math} x^4 y^5 z^6 \end{math}
More complicated exponents:	\begin{math} y^{15x} \end{math}
Fractional exponents:	\begin{math} x^\frac{1}{3} \end{math}
Fractions with exponents:	\begin{math} \left( \frac{x}{x+1} \right)^5 \end{math}
Higher roots	\begin{math} \sqrt[3]{x+6} \end{math}
Add rational expressions	\begin{math} \frac{x+5}{y-3}+\frac{y+5}{x+5} \end{math}

Sample Question 1. Type this:

I can't figure out how to factor \begin{math}2x^2+3x+1\end{math}.  
What should I do with the 2 at the start?

And you will see:

I can't figure out how to factor .  
What should I do with the 2 at the start?

Sample Question 2. Type this:

I'm trying to find the LCD for \begin{math}\frac{3}{x^2+x} - \frac{x+1}{x^2}\end{math}.
I think it should be \begin{math}x^2+x\end{math}, but I can't figure out what to 
multiply the second fraction by.  What should I do next?

And you will see:

I'm trying to find the LCD for .
I think it should be , but I can't figure out what to 
multiply the second fraction by.  What should I do next?