Fractions and roots

After powers, fractions and roots are the shapes you will type most. Both are a command followed by braces, and both grow to fit whatever you put inside.

Fractions with \frac

\frac takes two pairs of braces: the top first, then the bottom. \frac{1}{2} gives $\frac{1}{2}$, and \frac{a+b}{c} gives $\frac{a+b}{c}$.

Everything on top goes in the first pair of braces and everything underneath in the second. Without braces, LaTeX takes one character for each part: \frac12 still gives $\frac12$, which you will see often, but \frac ab+c gives $\frac ab+c$, with only the a and the b in the fraction. Writing the braces is never wrong.

Fractions inside fractions

A fraction can sit inside another one, top or bottom:

Inside a sentence, a fraction is drawn smaller so it fits the line, as in $\frac{1}{2}$ here. \dfrac keeps it full size, $\dfrac{1}{2}$, and \tfrac makes it small anywhere. In a formula on its own line, \frac is already full size.

Slash fractions

Sometimes a fraction is better on one line: in a power, or in running text. Type a slash: a/b gives $a/b$, and e^{x/2} gives $e^{x/2}$, which is easier to read than a stacked fraction squeezed into the power.

Square roots with \sqrt

\sqrt{...} puts its contents under a root sign, and the sign stretches over all of it: \sqrt{2} gives $\sqrt{2}$, and \sqrt{x^2 + y^2} gives $\sqrt{x^2 + y^2}$.

Other roots

For a cube root or any other, put the number in square brackets before the braces: \sqrt[3]{8} gives $\sqrt[3]{8}$, and \sqrt[n]{x} gives $\sqrt[n]{x}$.

Everything together

The quadratic formula uses all of it: a fraction, a square root, a power and \pm for plus or minus.

Practise

In short

• \frac{top}{bottom} makes a fraction, and fractions can sit inside each other.
• \dfrac keeps a fraction full size in a sentence; a slash keeps it on one line.
• \sqrt{...} makes a square root, and \sqrt[n]{...} any other.

Next, in lesson 4: Greek letters and the symbols that are not on your keyboard.