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.
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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