A fraction is a rational number expressed in the form $\frac{n}{d}$ or $n/d$ where $n$ is designated the numerator and $d$ the denominator. The slash between them is known as a solidus when the fraction is expressed as $n/d$

The fraction $n/d$ has value $n \div d$ For instance, $3/2 = 3 \div 2 = 1.5$

If $n$ and $d$ are positive, and $n/d < 1$ then $n/d$ is known as a proper fraction. Otherwise, it is an improper fraction. If $n$ and $d$ are relatively prime, then $n/d$ is said to be in lowest terms. Each rational number can be expressed uniquely as a fraction in lowest terms. To get a fraction in lowest terms, simply divide the numerator and the denominator by their greatest common divisor: $$\frac{60}{84} = \frac{60 \div 12}{84 \div 12} = \frac{5}{7}.$$

The rules for manipulating fractions are \begin{eqnarray*} \frac{a}{b} & \qquad = \qquad & \frac{ka}{kb}\\ \frac{a}{b} + \frac{c}{d} & \qquad = & \frac{ad + bc}{bd}\\ \frac{a}{b} - \frac{c}{d} & \qquad = & \frac{ad - bc}{bd}\\ \frac{a}{b} \times \frac{c}{d} & \qquad = & \frac{ac}{bd}\\ \frac{a}{b} \div \frac{c}{d} & \qquad = & \frac{ad}{bc}. \end{eqnarray*}