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Negative number

You write a negative number with a minus sign (−) to show that the value is less than zero.



We don't know exactly what negative numbers really are. Only for positive numbers we can imagine what they mean. Mathematicians don't care about it. But note: strange things can happen. We agree to write negative numbers with a minus sign, so


means that there are 2 things less than zero, whatever that may be. We never write +3 if we have three real things, but it is possible. We start with the addition of

Here we use brackets, because otherwise you can get confused. That went well, so we now continue with subtraction of

Do we really still know what we are doing? We have 6 things and subtract 4 things that are not there, from it and obtain 10. So effectively we have added 4. Let's look at this carefully and write everything in detail

Now once more with negative numbers

That is just fine. Now we subtract again

It is getting clearer. The brackets don't really help much, so we omit them

If you have a – followed by a + it gets negative. And the reverse, first a + and then a – works just the same. You have a – and another – then it becomes positive. That is of course quite strange if you think about it. In a multiplication it is the same, so

and we understand that now. We continue with a multiplication with negative numbers, where we use brackets for clearness

The result is positive, because the same rules apply. In a division it is also the same, so

As we understand this, a difficult calculation can be solved

The same rules apply to exponentiation, so

You should look carefully at this, as brackets play an important role here. There are some restrictions when using negative numbers. You will notice this when taking the root of a negative number

as it has no real value. To be precise

You must always apply the rules

 + + = + 
 + – = –
 – + = –
 – – = +



In the book Nine Chapters of the Mathematical Art compiled from the 10th century BC by various Chinese mathematicians, positive numbers are written in red and negative numbers are black.

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