Matrices

Explore how LaTeX makes formatting fractions and binomials easy and professional. Whether you're writing equations, ratios, or combinatorial expressions, LaTeX ensures everything looks clear and well-structured. In this section, you'll learn simple commands to create fractions and binomial coefficients effortlessly.

Fractions

Fractions are a fundamental aspect of mathematical expressions and LaTeX provides powerful tools to format them with precision.

Basic fraction syntax

In LaTeX, the \frac command is used to create fractions:

\frac{numerator}{denominator}

For example:

\[
\frac{3}{4}
\]

Output:

fraction example

Inline vs. display fractions

Fractions can be used in inline or display mode. LaTeX automatically adjusts the size of fractions based on the context:

  • Inline mode : $ \frac{numerator}{denominator} $ → The fraction appears smaller to fit within the text.
  • Display mode : \[ \frac{numerator}{denominator} \] → The farction is larger and more readable.

Here’s an example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\noindent Here is an example of a fraction in inline mode: $x = \frac{a}{b}$. Now, let's display the same fraction in display mode:

\[
x = \frac{a}{b}
\]

\end{document}

Output:

inline vs display math mode fraction example

You can also control the size of fractions by using the following commands:

  • \tfrac{} → text-style fraction, smaller
  • \dfrac{} → display-style fraction, larger

If you need more control over fraction sizes, LaTeX provides \tfrac{} for smaller text-style fractions and \dfrac{} for larger display-style fractions.

Here’s an example of using \tfrac and \dfrac commands:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\verb|\tfrac| output: $\tfrac{a}{b} $

\verb|\dfrac| output: $ \dfrac{a}{b} $

\end{document}

Output:

small and large fraction command example

Continued fractions with \cfrac

For continued fractions, use \cfrac{} from the amsmath package. Here’s an example:

\[
x = \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4}}}}
\]

Output:

continued fraction example

Here’s another example of continued fraction for the Golden Ratio:

\[
\varphi = 1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \dots}}}}
\]

Output:

continued fraction of golden ratio example

Binomial coefficients

Binomial coefficients are used to represent the number of ways to choose 𝑘 elements from a set of 𝑛 elements. In LaTeX, the binomial coefficient is written using the \binom{} command from the amsmath package:

\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]

Output:

binomial coefficient example