78/274 simplified

It's an intresting question, though. 

Simplifying rational numbers w/ several digits in both the numerator and denominator, by hand, is certainly not somthing every adult know how to do. And one can learn A LOT from such problems: the times table, divisibility rules, prime numbers, coprimes, and so forth. But, indeed, many calculators solve this instantly.

Questions involving simplifying rational numbers occur pretty often, so parhaps it should be included in "Great Answers to Learn From" or sth. I haven't looked into the matter yet...

You can evaluate this using the on-site calculator.

Well, both the denominator (bottom) and numerator (top) is even numbers (divisible by 2), so you can divide them by 2. You'll get:

39/137

Since the digit sum of the numerator is divisible by 3, the whole number must be divisible by 3. What about the denominator? Nah, it's digit sum is 11, so the whole number isn't divisible by three. 

But, we have nontheless gotten further in our solving. Since 39 is divisible by 3, we can much easier factorize it:

39/ 3 = 13       =>     3*13 = 39

Now all we have to do is to check if 137 is divisible by 11. (We have already checked for 3). 

No. 137 isn't divisible by 11. 

Since 39 and 137 doesn't have any factors in common, the simplest version of the original fraction is:

39/137

I'll probably refer to Wolfram Alpha for any related questions in future posts.