Definition of fraction

A formal definition of fraction is the following : A number that can be represented by an ordered pair of whole numbers  a / b , where b is not equal to zero.

For example, the following numbers are fractions.


A common misconception is to define fractions only as a part-to-whole model. It is true that initially, fractions were used to indicate the number of parts of a whole to be considered.

In the figure below, only two parts of the whole glass contain liquid.

Since the glass is divided into 3 equal parts and only 2 parts contain liquid, we use the fraction 2/3 to represent the 2 out of 3 equal parts.

Two-thirds full
Two-thirds full

However, as long as b is not zero, the definition of fraction allows us to choose any values for a and b. Therefore, a could be 5 while b could 3 and the fraction will be 5/3.


Notice that  the 4/0 is not technically a fraction because division by zero has no answer. And that is the reason the definition above says that b cannot be 0.

Recent math words

  1. What Does Divisible Mean? Definition and Examples

    Jan 09, 19 04:18 PM

    What does divisible mean ? A number is divisible by another number if ...

    Read More

  2. How Big is 1 Foot ? Definition and Examples

    Jan 09, 19 12:41 PM

    What is 1 foot ? 1 foot is a unit of length in the customary ...

    Read More