# Hans Gilde’s weblog

## Why a negative times a negative is a positive

Posted in mathematics by Hans on September 30, 2009

A few blogs have discussed an intuitive explanation of why multiplying two negatives produces a positive. That would be an explanation which  makes sense to a non-mathematician.

The most intuitive argument from those blogs, to my mind, was from The Math Less Traveled and talks about a negative as a reflection about zero on the number line (image of this at The Number Warrior).

Here is how I’d explain it:

The first question to be asked is: What is a negative value? Like what does $-3$ really mean?

The answer: A negative value, let’s say $-x$, is exactly a value where $x+(-x)=0$. That’s formally an additive inverse.

Now let’s look at $(-x)(-y)$. If we can believe that $(-x)(-y)=-(-(xy))$ then we’re in good shape.

What does $-(-(xy))$ mean? Per above, it means the number that, when added to $-(xy)$, equals zero. And that is obviously $xy$.

## Intersting Wolfram Alpha query

Posted in mathematics, statistics by Hans on September 13, 2009

I have previously been underwhelmed by Wolfram Alpha. But today I finally saw a real-life query produce good results.

Admittedly, I am probably in the minority of people excited by this: I was wondering how many megawatt hours are produced by 8000 tons of oil. And what do you know, the query on Alpha worked.

Thanks, Wolfram researchers.