Why does a negative number multiplied by another negative number give a positive number?
Anyone know, other than we were told this by our teachers, but why is it so?
it's the law
Imagine the number line. Suppose on the left it starts -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, etc.
Let's calculate 2 x (-3).
The expression -3 says starting at zero, go left 3 steps. The expression 2 x means do it twice.
Where do you finish? -6
If you see why you finish on the left side, you have your answer.
What about minus x minus. Let's calculate (-2) x (-3).
Again -3 says starting at zero go left 3 steps. The expression -2 x means, no, go the other way instead -- twice.
Where do you finish? +6. Minus x minus = plus.
It just is ok!!!!
still think its a crud answer
http://hartvig.com/2006/8/21/simple_math_minus_multiplied_minus_equals_plus.aspx
Right time to go home...
if you say -6 x -4 and you think of it as having
-6 groups of -4.
thats -(-4) -(-4) -(-4) -(-4) -(-4) -(-4)
then if you say double negative is positive for each of the pairs of - signs then you have
+4+4+4+4+4+4=24
[Edited on 7/10/08 by liam.mccaffrey]
mathematical law, (-) x (-) = (+)
god i love WIKI answers
minus times a minus equals a plus linky
it has to be the most un-mathematical answer ever!
[Edited on 7/10/08 by omega0684]
So if I go into the garage and say.. I've got -3 engines over there and I'm sure theres another -2 somewhere when I come back will there be 6? but how do I do the X thing practically to make 6 engines happen?
For the same reason that a negative balance is an overdraught and a negative overdraught is a positive balance.
A lack of a lack is a positive balance.
That's not maths, just logic.
@ coozer
if you owed someone 3 engines you would have -3 engines. so if you then owed someone 3 engines minus 2 times, then you would indeed find yourself owed
6 engines
So..........if I have -£100 in the bank , and spend -£100 twice , I will then have +£100
I think I need to go and have a word with my bank manager 
If you think that's a bit of a mystery you should try a bit of Ethiopian Shamen multiplication.
Pick two numbers which would be difficult to multiply in your head. Works with any number.
Eg 21 x 31. Put one number in the left column and one in the right. In the left column half the number and write the new number underneath. Forget
1/2's they don't exist (eg half of 17 would be 8, because 8.5 doesn't exist??) and keep doing this till you get to 1.
In the right hand side column keep doubling the number and writing it underneath so you have as many rows as you do for the first number.
Then, in the left column cross out any even numbers on account of them being "evil" and cross out their corresponding number in the right
column.
Then add up everything in the right column that hasn't been crossed out and you have your answer.
Eg.
21 x 31
10..........62 - discard this line as it's evil
5............124
2............248 - discard this line as it's evil
1............496
So you add, 31, 124 and 496 = 651 which is 21 x 31.
Weird eh!!!
[Edited on 7/10/08 by eznfrank]
quote:
Originally posted by liam.mccaffrey
@ coozer
if you owed someone 3 engines you would have -3 engines. so if you then owed someone 3 engines minus 2 times, then you would indeed find yourself owed 6 engines
quote:
Originally posted by clairetoo
So..........if I have -£100 in the bank , and spend -£100 twice , I will then have +£100
I think I need to go and have a word with my bank manager
quote:
Originally posted by liam.mccaffrey
quote:
Originally posted by clairetoo
So..........if I have -£100 in the bank , and spend -£100 twice , I will then have +£100
I think I need to go and have a word with my bank manager
Claire you are exactly right, if you spent -£100 twice your bank balance would increase by £200
double negative = postive no means yes and all that...
so here you go
if 2 to the power 2 (2x2) is 4
2 to the power 3 (2x2x2) is 8
whats 2 to the power 0
anything to the power of 0 is 1
quote:
Originally posted by liam.mccaffrey
anything to the power of 0 is 1
^^
quote:
Originally posted by mookaloid
it's the law
quote:
Originally posted by 24vseven
quote:
Originally posted by liam.mccaffrey
anything to the power of 0 is 1
again why
quote:
Originally posted by Alan B
quote:
Originally posted by 24vseven
quote:
Originally posted by liam.mccaffrey
anything to the power of 0 is 1
again why
X^2 x X^2 = X^4 (exponents added)
X^2 /X^2 = 1
Following the first example 2+2=4
So, 2-2=0
Therefore X^0 = 1
i can see where this is going
(-4)^0.5=sqrt(-4)=sqrt(4) x sqrt(-1)=2i
and to finish
i=?
You all need to get out more, stop it all NOW and go and get some cars built.
right now i have nothing better to do
i (the sqrt of -1) is an imaginary number, and before anyone says "whats the point of imaginary numbers"they are incredibly important in all
sorts of fields like electrical and control engineering
I'm not playing any more
Ooh! imaginary numbers...
That way lie fractals and madness.
Neil
Well, I didn't expect 3 pages but we can see it is not that simple an answer.
The best I could come up with was this.
I tried to remember back to school and other than being told "it is the rule", cannot remember if it was ever proved or explained why.
Googling did not come up with anything I was happy with so I thought some more about this.
From my point of view, the problem arises with negative numbers and what they mean in the real world around us. It is not an easy concept to grasp,
and you won’t be alone as remember that one of the most powerful civilisations, the Roman Empire, had no negatvie numbers nor a 0.
In short, negative numbers in the world around us are just nonsense.
For example think of apples.
If you have 6 apples, I ask you how many apples you have, you count them and tell me it is 6.
Now if you have -6 apples, I ask the same question, what do you do? You try to count your apples and then what? You have no apples so do you say 0
since negative apples do not exist?
Clearly something is wrong here.
The explanation given for having a negatvie amount of anything is that you “owe” that number of items and comes into its own when you take a piece of
paper and start to write things down.
Let’s say you owe me 6 apples and have picked 10 apples from the tree in you garden. You decide you want apple pie for supper so sit down to work out
how many apples you can use. You have 10 but owe me 6, the 6 negative apples, which leaves you with 4.
So now it kind of makes more sense.
So back to the original question.
A negative number of something being multiplied a negative number of times? What exactly does “negative number of times” mean in the real world?
Just more nonsense as far as I can see.
But there is a proof. It relies on some simple artithmetic rules which are easier to identify with in the world around us.
a.0 = 0
(-a).b = - a.b
a – a = 0
a.(b + c ) = a.b + a.c
So using the above:
-a.0 = 0
substitute b – b on LHS for 0 gives
-a( b – b ) = 0
expand:
-a.b + x = 0.
x is the result of multiplying two negative numbers: (-a).(-b) which is what we are trying to determine.
For the equation to balance, x must have value a.b
Therefore (-a).(-b) must be equal a.b
Not sure if that is a great proof but the best I can come up with.
It may not make a lot of sense in the real word but keeps mathematics happy.