any brilliant people out there..... how?!?!?

Question

okay even my math teacher cant explain to me how a negative multiplied by a negative equals a positive

can anyone make real sense of that?

Answer 1

Forget the hows and whys - just accept the logic and learn multiplication / addition etc before you get sidetracked into doing research when you should be working on your school assignment. So beware and dont go astray lest you fall back on your studies and flunk !!

Answer 2

There are several ways you can approach understanding this. I'll go through a couple; hopefully one of them will make sense to you.

Do you understand how a negative multiplied by a positive, or a positive by a negative, results in a negative? If so, that helps. For instance, if you're happy that 2 × -3 = -6, you can think of -2 × -3 as being the same as - (2 × -3) = - (-6) = +6.

This assumes a more fundamental concept that you also need to understand: the negative of a negative number is a positive number. To understand this it's best to replace "negative" with "opposite": the opposite of a positive number is negative, the opposite of a negative number is positive.

So when we're multiplying two negatives, we're taking the opposite of one (positive) number and multiplying it by the opposite of another one. If we were adding them this would mean we've got some "opposite" and then some more "opposite", so we'd wind up with a lot of "opposite" (you can see this is a highly scientific discussion!): for instance, (-3) + (-4) = -7.

However, by multiplying we're taking an "opposite" number of an "opposite" value, just like when we multiply positive numbers (e.g. 3×5) we are taking three lots of 5. So in this case we're applying the "opposite" operation to something which already has had the "opposite" operation applied. In other words, we're taking the opposite twice so it flips us back to where we started.

Another way to think about it is using the common analogy of a bill or debt (note: here I am using "bill" to mean the type that has to be paid, not a banknote) for a negative amount of money. Suppose you had $500 and I sent you three bills each for $100. Then you would have $200 left; I've given you 3 × -$100 = -$300. But suppose I then realised I gave you three copies of the same bill and took two of them back - that is, I now gave you (-2) bills for $100. Now you only have one bill, so you have $400 left; by giving you (-2) amounts of (-$100) I've effectively given you $200.

There are various other analogies that we could use, but in the end they all boil down to the same thing: whatever the analogy for a positive is, the analogy for a negative will be the reverse. By multiplying two negatives you are reversing the outcome twice, and the two reversals cancel out, leaving you with a positive.

Answer 3

Sure, I'll try

Say we have two numbers A and B, if they are negative we can write them as:
A = A*(-1)
B = B*(-1)

so (-A)*(-B) = A*B*(-1)*(-1)

so what is (-1)*(-1) ?

well it is chosen to be +1. If you pick something else you lose certain properties of multiplication like the distributive property.
Say we pick (-1)(-1) = -1
(-1) * (3 - 3) = (-1)(3) + (-1)(-1)(3)
0 = -3 + (-1)(3) = -6
Now zero does not equal -6, because the distributive property is a good thing to have you should choose (-1)(-1) such that it works.

I hope this makes sense.

Answer 4

How about a pattern?
3 x 4 = 12
3 x 3 = 9 . . . . . (12 - 3)
3 x 2 = 6 . . . . . (9 - 3)
3 x 1 = 3 . . . . . (6 - 3)
3 x 0 = 0 . . . . . (3 - 3)
3 x (-1) = -3 . . .(0 - 3)
3 x (-2) = -6 . . .(-3 - 3)
This pattern shows
Pos x Neg = Neg

By commutative property
Neg x Pos = Neg
(-3) x 4 = -12
(-3) x 3 = -9 . . . . .(-12 + 3)
(-3) x 2 = -6 . . . . .(-9 + 3)
(-3) x 1 = -3 . . . . .(-6 + 3)
(-3) x 0 = 0 . . . . . .(-3 + 3)
(-3) x (-1) = 3 . . . .(0 + 3)
(-3) x (-2) = 6 . . . .(3 + 3)
This pattern shows
Neg x Neg = Pos

Answer 5

I know it's not apparent right away, but if we're using the math for real life reason, the agreement that (-1)*(-1) = 1 ... works.

Here's a page that explains many ways: http://mathforum.org/dr.math/faq/faq.negxneg.html

Say you pay car insurance, $40 per month. That's -40 dollars to you. Say I lose a bet, and I have to pay your car insurance for 3 months. That's -3 months of paying insurance for you. So, -3 months of -40 dollars = $120 you won on the bet.

So my guess is it's something derived from real world applications. It works.

Answer 6

When all the rules of math were set up a long time ago (wish I could tell you when), thats what they decided. They decided your order of operations is PEMDAS and they decided this was the way it would go as well.

Math would work just fine if two negatives equaled a negative, just as long as everyone who does math agrees to those rules.

P.S. I don't know what level of math your in, but the rules suck more and more the further you go.

Answer 7

Example: Let's say you have 100 coins, 3 persons and 5 coins that this 3 persons are going to take away from your 100 coins.

= 100 - (+ 3 * + 5)
= 100 - (+ 15)
= 100 - 15
= 85

Let's reverse the situation: the 3 persons instead of taking away 5 each are going to add up 5 each to the 100 coins you already have.
= 100 - (- 3 * + 5)
= 100 - (- 15)
= 100 + 15
= 115

I hope I helped with this.

Answer 8

Okay my math teacher told me this in 7th grade. When a positive and positive are together their happy (positive) When a negative and a positive are together there mad cause they don't like each other (negative) But when a negative and a negative are together their happy!!(Positive) Its just a basic law in math that cant be messed with.

Answer 9

because since theres 2 negative it equals a positive :D
cause like uhm when you add 2 negatives it equals a negative but when multiply and divide it equals a positive.
cause since they are the same sign that you are multiplying then you keep the sign.
but if they are different signs then the bigger gets the sign's answer.

Ya digg?

Answer 10

5 x 6 can be said as "five groups of six." If you have a NEGATIVE amount of groups, it would be something like "A lack of five groups lacking in six," so because of the double negative, if you're missing a lack of something, it means you have something.

Does that make sense? I tried to explain it as clearly as possible, but it's all about word choice.