Quick Way to Do Common Kind of Problem?

[fireemblem13]

I've seen these problems a lot. I solve them using my way and end up taking more time than I probably should. Problems in the form:
a * a / b

[mathslug]

Here's an example:

17 * 17/19

The answer is in two steps. The fractional part of the answer is equal to the difference in the two different numbers squared over the denominator. The whole number is equal to the numerator (a) minus the difference between the two numbers.

So...

that means that the fraction equals (19-17)^2 / 19 = 4/19
the whole number = 17 - (19-17) = 15

Answer = 15 4/19

[AuSmith]

And, things like [unparseable or potentially dangerous latex formula] also come up. It's the same deal; you just add the difference instead of subtracting it.

Just an identity.

[unparseable or potentially dangerous latex formula]

Also, you should write the fractional part down first, since it's not always proper. e.g.

[unparseable or potentially dangerous latex formula]

and the problem lies in that you can't write [unparseable or potentially dangerous latex formula] and get it correct. These situations are where skilled markovers are handy. Hahaha.

[Kurt]

Edit: hahaha, just posted same thing as above.

[AuSmith]

wrong thread, irrelevant post.

[stupidityismygam]

come on guys, use [unparseable or potentially dangerous latex formula]

Example:

[unparseable or potentially dangerous latex formula]

[AuSmith]

Yea, sry. I didn't know LaTeX was enabled.

[stupidityismygam]

hey AuSmith for mods you can do

\equiv for congruency
so

[unparseable or potentially dangerous latex formula]

[AuSmith]

Cool. I wonder why it's common to use the triple bar for modular arithmetic. It's already overloaded, and as far as I know, it means the same as equals in this situation.