Maths question

jp_bl_68

jp_bl_68

jp_bl_68

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This might be a stupid question but my brain's too frazzled to know for sure. Why when two minus numbers are multiplied do you get a positive number?




(awaits obvious answer followed by cruel, yet justified, mocking)
 
It just does :p

Imagine it in terms of.. let's say money in an account, so we can have negative values.

2 x £2 is two groups of £2, so we have £4.

-2 x £2 means we take away two groups of £2, so we have -£4

-2 x -£2 means we are taking away a negative, i.e. adding money, so we have £4.

Also, lol.
 
It's quite difficult to imagine if you try put it in a real life scenario.. (apart from the above :/)..

It's just a rule that you should stick to..

.. tbh, you could boil that question down to why does add mean add? :s
 
I think that's a great question OP.

He's after an explanation of the mathematical theory that causes two negative terms to equate a positive product. Rather than choosing to accept.
 
The way I remembered it when doing maths at school is that the two - - combine together to make a +. In my head theres a little animation where one of the - flips 90 degrees.

Couldnt tell you why thats the rule though!
 
Multiplying something by a negative is just like saying 'what's the opposite of it'

What's the opposite of -2?
+2

What's 2 lots of the opposite of -2?
+4

Also consider that -1 is another way of saying -1 x 1, another way to say -2 is -1 x 2...
 
Basically, any other method would cause something else to break.

E.g., if -1 * -1 = -1:

(-1)(1 + -1) = (-1)(1) + (-1)(-1)

(-1)(0) = -1 + -1

0 = -2

Doesn't work (the example was copy pasted).
 
D D Danneh said:
It just does :p

Imagine it in terms of.. let's say money in an account, so we can have negative values.

2 x £2 is two groups of £2, so we have £4.

-2 x £2 means we take away two groups of £2, so we have -£4

-2 x -£2 means we are taking away a negative, i.e. adding money, so we have £4.

Also, lol.
Click to expand...

Sweetly put. :D
A minus of a minus is a positive. But I preferred the way you put it.


EDIT: you are going to get someone asking why doesn't a + times a + give a minus then?
 
trentlad said:
I think that's a great question OP.
Click to expand...

I'd agree with that

It is Distributivity (and the fact that multiplication is distributive) that dictates that (-1 x -1) must equal 1.

Distributivity means that if you multiply a whole load of numbers by Y and then add them up, you get the same answer as if you added them all up first and then multiplied that sum by Y i.e. 2x(1+2+3+4) = (2x1)+(2x2)+(2x3)+(2x4)

And now the proof (Requires that you believe/understand that (-1 x 1) = -1 :))

Consider the equation -1 x (1 + -1 + 1) = ?

First you add up the bits in the brackets and you get (1 + -1 + 1) = 1

Then you multiply by -1 to get the answer (-1 x 1) = -1

Now try employing distributivity to do it the other way

You would get:

(-1 x 1) + (-1 x -1) + (-1 x 1) = ?

See you have a (-1 x -1) bit in the middle. Assuming (-1 x -1) = -1 you would get the following:

-1 + -1 + -1 = -3

Which is different to the answer for the way the equation was previously arranged.

The only way it will work is if (-1 x -1) = 1, as below, thus fulfilling the requirement that multiplication is Distributive.

-1 + 1 + -1 = -1
 
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jimmy is on the money.

Any other definition would cause unexpected and inconsistent results.

If you find it hard to understand, just accept that that's the way it's defined, and use it as a rule. Like all maths stuff, things normally become very clear with a bit of familiarity.:)
 
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TBH I didn't know the answer either and had to google hard as it was annoying me! Couldn't find a very useful explanation anywhere so did my best to make it clear and simple. My work is starting to require that I do more and more maths so have been going through old books lately so was in the mood for it :)
 
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