Maths question
- Thread starter jp_bl_68
- Start date
Soldato
Because that's how multiplication is defined.
Associate
Soldato
It just does 
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.
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.
Associate
++ = +
+- = -
-+ = -
-- = +
It just does!
+- = -
-+ = -
-- = +
It just does!
Associate
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
It's just a rule that you should stick to..
.. tbh, you could boil that question down to why does add mean add? :s
Pretty much. Thanks for all the "It just does" answers, very helpful
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...
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...
Caporegime
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).
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).
Soldato
It just does
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.
Sweetly put.
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?
Associate
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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That cleared things up a bit, cheers.
Soldato
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.
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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Associate
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