1. ## Algebra proof- help!

I need to prove this:

If A is divisible by B, the the quotient (a/b) is the number of mutiples of B from 1 to A.

ex:

10/5= 2, therefore 10 has 2 multiples of 5.

I don't know what theorem's to use or how to start it. Can anyone help? Thanks a lot!

2. I think you need to perhaps revise your wording.

If A is divisible by B, the the quotient (a/b) is the number of mutiples of B from 1 to A.
This just sounds like division to me. I'm not sure how you would go about proving division.

3. ## well

it kind of is actually.
I'm trying to figure out and prove, more so, that the quotient is the amount of multiples in A of B.

4. ## hi

hi

I dont really understand what you mean here.

In simple division: $\displaystyle \frac {a} {b} = X$
And X times will b "fit" into A.

Like your example: $\displaystyle \frac {10} {5} = 2$
5 goes two times into 10.

Try to specify your problem a little better.

5. Can you just rewrite $\displaystyle \frac{a}{b} = X$ as $\displaystyle a = b * X$, and so a is b multiplied X times, i.e., X multiples of B?

Since you're dealing with division but want to think about it in terms of multiplication, change your division problem into multiplication, as above.

However, all of this is just a different way of describing division - I wouldn't call this a proof, rather just looking at division from a different angle.

6. agreed

7. Originally Posted by Mathnasium
However, all of this is just a different way of describing division
It isn't a different way of describing division, it is the way that division is defined when deriving the rational number system.

-Dan