Why does minus minus a minus equal a minus?

Answer 1

Minus minus a minus does not necessarily produce a minus answer.

Here is an example of a minus figure, minus another minus figure:

-3 - (-5) = -3 + 5 = +2

As long as the absolute value of the first number is smaller than that of the second, the final answer will always be positive.

If the two are equal, the final answer is 0:

-4 - (-4) = -4 + 4 = 0

Only if the magnitude of the first is larger than the second is the answer negative: -3 - (-2) = -3 + 2 = -1

-------------------------------------------------------------------------------------------------------

HOWEVER, if we are trying to determine the sign of a number that has multiple signs, for example (-3), -(-3), or -(-(-3)), [minus, minus a minus] then the logic is this:

A negative is a negative, so -3 is negative, and means deduct 3

A negative negative is a positive, so -(-3) is positive and means add 3

A negative 'negative negative' is a negative, so -(-(-3)) [i.e. minus, minus a minus] is negative and means minus 3

Let's work it through another way:

If minus n means minus n

Then minus (minus n) must mean plus n

Therefore minus (minus (minus n)) must mean minus n

Yet another way to think of it:

If you add a minus figure to a calculation, you deduct it.

But if you deduct a minus figure, you must ADD it (thereby reversing its original 'negativity' and the figure become a positive one)

So if you have to then 'minus' it once more, (thereby reversing its positive status) it has 'minus' value again.

Method of determining the signIf you have a formula with 'stacked' minuses, remove them in pairs, starting from the left. If you've got one left, the resulting value will be a minus figure. But if 'pairing' them removes them all, then the remaining figure is positive, i.e. '+'.