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Guide for this category...
I've considered putting negative numbers earlier on the map than they are, immediately after subtraction is introduced. They're abstract enough, however, that they're currently down here.
A negative number is simply the equal opposite of a regular number. The normal basis for explaining this is a number line.
Positive numbers are on the right side of 0, and are reached by adding; negative numbers are on the left and are reached by subtracting. You could say that the negative number is the result of 0 - the given positive number.
The main difficulty in negative numbers is that adding and subtracting them can be counterintuitive, particularly when they're in problems with positive numbers. Have a look at the following equations, which illustrate the dynamics.5 + 4 = 9
5 - 4 = 1
5 + -4 = 1
5 - -4 = 9
-5 + -4 = -9
-5 - -4 = -1
-5 + 4 = -1
-5 - 4 = -9
The minus sign here is logically similar to the word 'not'. As in English, a pair of negatives cancels each other out; if you say that you will not not do something, that means you will do it. But if you will not not not do it, you're back to one not, and so you won't. This effect will come up again in a spectacular and confusing way in Negative Numbers 2, but for now, enjoy adding and subtracting.