Academic questions...

use a shredder

 

Yeah. Sorry about that. I'm useless at maths but half decent at finding information. This any use:

http://www.mathwizz.com/fractions/help/help4.htm

 

Long Division. It's easier than you think.

 

I suck at math XD

 

I just don't reduce them, if I can get away with it. If I know how to come up with the answer, then whoever is looking at the result can reduce their own damn fraction if they're that particular

 

Factoring really isn't that bad. You just have to know the trick for 2, 3, 4, and 5. You'll rarely need anything higher.

Wow, Euclidean Algorithm! I completely forgot about that! Great find!

 

Well, there are a few:

Even numbers can be factored by two.
If you add both digits together and that number is divisible by three, then the original number is divisible by three (63 --> 6+3=9 --> 63 is divisible by three)
I forget the rule to four, but that's okay cuz I never check for four anyways.
If the number ends in a 5 or 0, it is divisible by five.
If a number is divisible by both two and three, then it is divisible by six.

 

You don't really need a trick for 4. If it's divisable by 4 just use 2, since they're both even.

 

^^ That's what I always do. There's really not much point in checking.

There is a pattern with four, like all the other numbers, that's not too hard to figure out:
4, 8, 12, 16, 20 || 24, 28, 32, 36, 40...
ends in: 4, 8, 2, 6, 0 || 4, 8, 2, 6, 0...
So if it's divisible by four, it would end in one of those numbers, in increments of 20