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

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) (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
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Cheers,
Stan H.
Answer by solver91311(24713) (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. 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 as .

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

So let's divide by => . 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: . But from the first rule we talked about above .

Therefore .

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 reciprocal is also called the multiplicative inverse.

So, if you are dividing a by b , it is the same as multiplying a by the reciprocal of b . Now we can define some and our division becomes a straight multiplication: , 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

We can write

(factor out -a)

Also,

(factor out b)

So we have

and

Hence, by the transitivity of equality, we have

Hope that helps.
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