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We know that A fraction represents a part of a whole or, more generally, any number of equal parts. So fraction can not be negative.$\frac12$ and $\frac{-1}{2}$ both are fraction number or not?

Soham
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user293607
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3 Answers3

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You can extend your "naive" or "intuitive" notion of a fraction to include fractions that are zero or negative as well.

A negative fraction could indicate the absence removal of the indicated quantity.

For example, adding $-1/2$ of a pizza would mean removing $1/2$ of that pizza.

So, yes, fractions can be negative.

MPW
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  • "absence" is the wrong word, as it means zero. – user21820 Dec 04 '15 at 02:44
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    @user21820: I meant it as a transition from "presence" to "absence" -- in other words, subtraction. I've reworded it -- better? – MPW Dec 04 '15 at 13:28
  • Yes it's better. I know that "absence" was meant to be in contrast to "presence", but whenever we want to talk about both positive and negative numbers together with the same consistent interpretation, "presence" would be wrong too. The whole concept revolves around the operation of adding or removing some quantity, instead of the actual amount present. – user21820 Dec 04 '15 at 13:37
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What is to be said here that you are thinking in a different way.To explain your thinking see this.

Let we have two parts,the whole part is represented by $1$ and you are going to take away $\frac12$ away from it.So remaining=$1-\frac12=1+(-\frac12)$.Thus we can see fraction can be negative.

Also,going by definition fraction is a rational number and it can be both positive and negative.

Soham
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You are using term "fraction" in rather intuitive terms, and in mathematics we want to first make everything we speak about precise, so that we can give a definite yes/no answer.

In this case, a precise notion of fraction generally used in mathematics is the notion of rational number, which is a number of a form $\frac{n}{m}$, where $n,m$ are integers and $m$ is not $0$. Since integers include negative numbers, it is possible for a rational number to be negative, for example, $\frac{-1}{2}=-\frac{1}{2}$.

Wojowu
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