SOLUTION: Hii. Well i was assighned a Essay to do that has to be about 1-2 pages of why do we get a positive number when deviding a negative number by a negative number? and a feww examples

Algebra ->  Signed-numbers -> SOLUTION: Hii. Well i was assighned a Essay to do that has to be about 1-2 pages of why do we get a positive number when deviding a negative number by a negative number? and a feww examples       Log On


   

Question 117632: Hii. Well i was assighned a Essay to do that has to be about 1-2 pages of why do we get a positive number when deviding a negative number by a negative number? and a feww examples and add diagrams and stuff. And i didnt really find any answers online. do u think you could help me?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use examples such as temperature, profit and loss, direction on
a number line, football yardage.
Make sure you define your terms: negative/positive, minus/plus, left/right,
down/up
-------------
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The simplest explanation that I can give is this:

If you divide any number by itself, you always get 1. a%2Fa=1 for all real numbers.

You can also express any negative number as the product of that number's opposite and -1. In other words, you could write -4 as %28-1%29%284%29.

Let's say that x is some positive number x%3E0 and y is some positive number y%3E0. Then we can say that -x and -y are negative numbers. (I hope you clearly understand why you can't just say -x is a negative number without qualifying x as positive in the first place.)

So let's divide -x by -y => %28-x%29%2F%28-y%29. But we already said that you can also express any negative number as the product of that number's opposite and -1, so we can write: %28%28-1%29x%29%2F%28%28-1%29y%29. But from the first rule we talked about above %28-1%29%2F%28-1%29=1.

Therefore %28%28-1%29x%29%2F%28%28-1%29y%29=%281%29%28x%2Fy%29=%28x%2Fy%29.

Now all you have to do is prove that the quotient of a positive number divided by a positive number is positive -- or just take that one on faith.

***************************
There is another way to do this. Remember that division is nothing more than multiplication by the reciprocal. A reciprocal is a number formed from an original number such that the product of the original and the reciprocal equal one. a%2A%281%2Fa%29=1 A reciprocal is also called the multiplicative inverse.

So, if you are dividing a by b a%2Fb, it is the same as multiplying a by the reciprocal of b a%2A%281%2Fb%29. Now we can define some c=1%2Fb and our division becomes a straight multiplication: a%2Ac, and our problem becomes one of proving that a negative number times a negative number yields a positive product.

Let a and b be any two real numbers.

Consider the number x defined by
x+=+ab+%2B+%28-a%29%28b%29+%2B+%28-a%29%28-b%29

We can write

x+=+ab+%2B+%28-a%29%28+%28b%29+%2B+%28-b%29+%29 (factor out -a)
x++=+ab+%2B+%28-a%29%280%29
x+=+ab+%2B+0
x++=+ab
Also,

x+=+%28+a+%2B+%28-a%29+%29b+%2B+%28-a%29%28-b%29 (factor out b)
x++=+0+%2A+b+%2B+%28-a%29%28-b%29
x++=+0+%2B+%28-a%29%28-b%29
x++=+%28-a%29%28-b%29

So we have

x+=+ab
and
x+=+%28-a%29%28-b%29

Hence, by the transitivity of equality, we have
ab+=+%28-a%29%28-b%29


Hope that helps.