Student Library

Fractions

3 min read

Displaying Fractions

  • There are two ways of displaying fractions in KaTEX: using \frac or \over
  • Depending on your use case, it might be readable to use one over the other.

Fractions with \frac

  • Using the \frac{}{} command allows us to display fractions.

    • Any math inside the first bracket is displayed in the numerator and any math in the second gets displayed in the denominator.

  • \frac{2x}{x + 1}

  • 1 + \frac{x^2 -1}{x^3 + x + 1}
  • \frac{1}{x} - \frac{2}{x + 1}

Fractions with \over

  • The \over command acts as a separator between the numerator and denominator.

    • Anything to the left is displayed in the numerator and anything in the right is displayed in the denominator.

  • 1+ 3x + 4x^2 \over 3x - 1

  • However, if we want a part of the expression to not include as part of the fraction, we would enclose the part that we want to include into our expression with grouping symbols {...}.

  • 1 + {3x + 4x^2 \over 3x - 1}

Variations in Displaying Fractions

  • Fractions are displayed differently in both inline and display math modes.

  • Inline math fractions are much smaller in size to fit the actual text size like , or .

  • Display math fractions are much larger and often intended for display.

  • f^{-1}(x) = \frac{2x-5}{1-x}

  • \frac{}{} automatically switches to inline fractions or display fractions depending on the math mode.

    • However, you can use \dfrac{}{} to force fractions in display mode.
    • Likewise, you can use \tfrac{}{} to force fractions in inline mode.

  • Here are some inline cases that uses \dfrac:

    • 1 - \dfrac{1}{2} + \dfrac{1}{3} - \cdots displays as
    • \dfrac{1 - x + x^2}{x^2 + x + 1} displays as

Here’s an example of a display case that uses \tfrac:

  • \tfrac{1}{x^3 - x} = \tfrac{A}{x} + \tfrac{B}{x-1} + \tfrac{C}{x+1}

Complex Fractions

  • We can create complex fractions by nesting combinations of \frac’s or \over’s.

  • \frac{1 + \frac{1}{2}}{3}

  • 1 + {\frac{1}{a} - \frac{1}{b} \over \frac{b}{a}}

  • By default, fractions nested in the numerator or denominator are displayed in inline mode, even if the entire expression is written in display mode.

    • You can force them to display mode by using \dfrac.

  • \frac{1}{1 + \frac{1}{2 + \frac{1}{3 + \cdots}}}

  • \frac{1}{1 + \dfrac{1}{2 + \dfrac{1}{3 + \cdots}}}

Graph View