Fractions » What is a fraction?

General information

A fraction is nothing less than a number. You can therefore indicate fractions on the number line. A fraction is the outcome (quotient) of a division of two integers. Integers are whole numbers. For that reason you should never leave a decimal number in a fraction. You can also say that a fraction is the ratio between two numbers.

Examples are 12, 34 and 13.

You can write fractions as decimal numbers.
However some decimal numbers will be infinite.
12 = 1 : 2 = 0.5
34 = 3 : 4 = 0.75
13 = 1 : 3 = 0.3333333333...

Numerator and denominator

A fraction always consists of a numerator and a denominator.
The numerator is the number above the division line and the denominator is the number below the division line.
In 34 the 3 is the numerator and the 4 is the denominator.

Unit fraction

A unit fraction is a fraction with a numerator of 1.

Proper and improper

A proper fraction is a fraction where the numerator is less than the denominator.
So a proper fraction lies between –1 and 0 and between 0 and 1.
Examples of proper fractions are 56 and –37.

An improper fraction is a fraction where the numerator is greater or equal to the denominator. Therefore, an improper fraction is less than or equal to –1 or greater than or equal to 1.
Examples of improper fractions are –65 and 77.

Mixed number / mixed fraction

A mixed number (or mixed fraction) is a number that consists of a whole number and a fraction.
For example: 112 and 1234.

Rational/Set

All the fractions together form the set of rational numbers.