Fractions, roots and sums

A maths toolkit: amsmath

For serious maths, load the amsmath package once in the preamble:

\usepackage{amsmath}

It adds better fractions, alignment, and dozens of symbols. Almost every maths document uses it.

$frac renders a stacked fraction, sqrt a root sign, and sum a big sigma$

Fractions and roots

A fraction is \frac{top}{bottom}; a square root is \sqrt{...}:

\[ \frac{a + b}{2} \qquad \sqrt{x^2 + y^2} \]

They nest happily: \sqrt{\frac{1}{n}} is the square root of one-over-n.

Sums and integrals

These grow to the right size automatically:

\[ \sum_{i=1}^{n} i \qquad \int_0^1 x^2 \, dx \]

The _ sets the lower limit and ^ the upper limit — the same keys as powers.

Common mistakes

\frac{a}{b}, \sqrt{x} and \sum only work in math mode.
Put them inside $...$ or \[ ... \].

Write a fraction in the display equation. Replace the comment with \frac{1}{2} so the equation reads one-half. The amsmath package is already loaded for you.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  % write a fraction here
\]
\end{document}

Click Run to compile and preview the PDF.

Now use two more maths tools. In the display equation write a square root \sqrt{...} and a sum \sum, for example \[ \sqrt{2} + \sum_{i=1}^{n} i \].

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  % write a square root and a sum here
\]
\end{document}