Question 23594
That's a great strategy- not wanting the answer I mean.
Ok, so whenever we want to add or subtract fractions, we need to start with a common denominator.  Sometimes this is already present (like 4/5 - 2/5), and sometimes we need to get our own (like 4/5 - 2/15).  If we have a common denominator, we simply combine the numerators (4/5 - 2/5 = (4-2)/5 = 2/5).  If we need to find our own, we have more cases.
The first is that one denominator is a factor of the other.  (5 is a factor of 15 since 3*5=15.  So for 4/5 - 2/15 we multiply 4/5 by 3/3, which we can do since 3/3 = 1, and get 12/15 - 2/15 =10/15 =2/3, our answer here).
Another possibility is that both denominators have a common factor. (If we have 2/10 + 4/15, we see 10=2*5 and 15=3*5, so we can get a common denominator of 2*3*5=30.  So we multiply 2/10 by 3/3 and multiply 4/15 by 2/2 and get 6/30 + 8/30 = 14/30 = 7/15).
Finally, it is possible that the denominators have no common factors.  (If we have -2/5 - 1/12, we see 5 and 12 have no common factors, so we can get a common denominator by multiplying 5 and 12 to get 60.  So, we multiply -2/5 by 12/12 and -1/12 by 5/5 and get (-24/60)+(-5/60)= -29/60).

*Note: IN this last case, we changed -2/5 - 1/12 to -2/5 + -1/12.

**Note: This last strategy of multiplying the denominators works in all cases, but in the previous cases it will give us unnecessarily large numbers to work with (With 2/10+4/15, we would get (2*15/10*15)+(4*10/15*10) = (30+40)/150 = 70/150 = 7/15).