Improper fraction - Definition

In algebra, an improper fraction is a fraction where the absolute value of the numerator is greater than the absolute value of the denominator. An improper fraction has the following form:

<math> \frac{p}{q} <math>

where p is an integer, which is divided by a non-zero integer q. For example:

<math>\frac{3}{2},<math><math> \frac{16}{3},<math><math>\frac{-8}{5},<math><math>\frac{4}{-3}<math> and <math>\frac{-9}{-7}<math>

are all improper fractions:

The improper fraction "seven divided by four", "seven over four", "seven quarters", or "seven fourths" can be written as

<math>\frac{7}{4}<math>

or

7÷4

or

7/4.

The line that separates the numerator and the denominator in the first case is called the vinculum.

The forward slash that separates the numerator and the denominator in the last case is called the solidus.

The denominator can never be zero because division by zero is not defined. All improper fractions are rational numbers and, by definition, all rational numbers can be expressed as vulgar fractions.