(some) reasons why 5 - -3 = 8
(i) with subtraction you can add the same amount to both bits (the minuend and the subtrahend) and it doesn't change the result; so add 3 to both: 5 - -3 = 8 - 0
(ii) it's the gap from -3 up to 5 on a number line
(iii) an equivalence class that can be adjusted by adding 'nothing':
(iv) extending a pattern:
5 - 3 = 2,
5 - 2 = 3,
5 - 1 = 4,
5 - 0 = 5
so 5 - -1 = 6,
5 - -2 = 7,
and so 5 - - 3 is 8
(v) using a straight line graph rule: continuing the graph of y = 5 - x into the negative quadrants you can see that when x = -3, y = 8
(vi) using inverses: 5 = 8 - 3 so 5 - -3 = 8
(vii) also using inverses: 8 + - 3 = 5 so 8 = 5 - -3
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