Why do we have fractions?

Answer 1

In terms of real life, it is because we want to know about parts of a whole, or how things can be shared.

In mathematical terms, the set of integers is not closed under division. In order that the set is a field, it is necessary to introduce rational numbers (or fractions).

The word fraction actually comes from the Latin "fractio" which means to break. It was used by the romans (although fractions as we now know them did not actually spread across Europe until the early /mid seventeenth century). Prior to this In ancient Rome, fractions were only written using words to describe part of the "whole". They were based on the unit of weight which was called the "as". Therefore, one "as" was made up of 12 uncia so fractions were centred on twelfths. Example:

1/12 was called uncia

6/12 was called semis

1/24 was called semuncia

1/144 was called scripulum

Answer 2

Quite simply, not everything can be expressed in whole numbers. As an example, the unit of length or distance is the meter; but you can easily imagine distances or lengths that are less than one meter.