[patton]

look for a least common denominator - the prime factorization of 3 is "3", and that of 4 is "2*2", so the LCD is "3*2*2", and thus "12". Mutiplying the numerator by the other primes as appropriate, we get "1*2*2+1*3" = "3+4" = "7". Note then that the prime factorization of the resultant numerator is "7", that of the denominator, "3*2*2", and that they have no factors in common, so the resultant needs no reduction, and the answer is "7/12".

This technique works for any two fractions, not just those that are so simple my dog could do it.

[napscoordinator]

Thank God I got it right! lol.

[leda]

yes, there's usually a complicated explanation
for the things i can figure out in my head, i just
like to keep it a secret. :D

[megatherium]

Here is a rather easier technique for adding two simple fractions: Remember the formula a/b + c/d = (ad+bc)/(bd). The trick is that you remember the formula by writing a/b + c/d in the usual vertical format and drawing a cross over the two fractions (so that the cross joins the a and d, and also the b and c -- that produces the numerator ad+bc). This works best for small fractions, in that the denominator bd may not be as small as the least common multiple of b and d. But it requires little work or thought to perform: just remember the cross pattern for the numerator, and multiply the denominators.

[dr_lew]

N and N+1 never have a common factor, so their LCM is always N*(N+1).
E.g. 104 = 2*2*2*13 and 105 = 3*5*7 .

Note also 1/N - 1/(N+1) = 1/( N*(N+1) ), which is a lot of fun.
Notice this provides a proof of the above!

[Darnright]

>look for a least common denominator - the prime factorization of 3 is "3", and that of 4 is "2*2", so the LCD is "3*2*2", and thus "12".<

Thanks for this. I reverted back to the way I learned in elementary school, but using least common denominators works so much better with harder fractions.

Ok, I admit it, I spent the entire year in the math lab getting through calculus (but, hey, I passed with a decent grade).