Negative number
You write a negative number with a minus sign (−) to show that the value is less than zero.
Explanation
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 parentheses, 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 parentheses 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 parentheses 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 parentheses 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
+ + = +
+ – = –
– + = –
– – = +
HistoryIn 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. |