First, I'm going to teach you how to get the sum of fractions with like denominators, then with unlike denominators, and then with mixed numbers:
LIKE Denominators:
Lets say the question is 1/5 + 2/5. All you have to do is add the numerator and the other numerator.
So, 1/5 + 2/5 = 3/5.
NOT: 1/5 + 2/5 = 3/10.
In adding with LIKE denominators you never add the denominators. Only the numerators it would make a BIG difference in your answer.
If your sum comes out to be an improper fraction, we have to change it into a mixed number which is putting it in lowest terms.
Lets say this was your answer: 8/5. Since the numerator is larger then the denominator it is called an improper fraction. To convert it back into a proper fraction. This is what you have to do:
Ask yourself "How many times does 5 go into 8?"
85=3.
5 goes into 9 one time. Then you take the 3 and put it over the 5. So your final answer should come out to be 1 3/5.
The same exact thing is with subtracting.
Lets say the question is 4/5  3/5.
All you have to do is  4 from 3. So that makes the answer 1/5!
UNLIKE Denominators:
When adding with Unlike Denominators, you first have to find something called the LCD (least common denominator).
So lets say the question is 3/5 + 2/4.
This is when we find the LCD.
5, 10, 15, (20),
4, 8, 12, 16, (20),
3/5 = /20
+
2/4 = /20
So now we have two denominators with no numerators. What we do to the bottom we have to do to the top so our problem now is 12/20 + 10/20. all you do is add across with the numerators and we now have 22/20.
22/20 is converted to 1 1/10.
Lets say there is a whole number  a fraction. This is what you have to do:
20

5/8
=
Alright, first we have to make 20 into a fraction, so to do that, we cross it out, and put a 19 above it. Because we are borrowing from it. Then we put 20/20 next to the 20. Now we subtract.
20/20

5/8
=
15/12.
Converted to 1 1/4.
Mixed Numbers:
Lets say the question is 5 1/3 + 3 1/4.
We have to find a LCM for 4 and 3 so that would be 12 so now its and whatever you do to the bottom you have to do to the top so its now
4/12
+
3/12
That would = 7/12.
Now, we go back and add 5 and 3 and that is 8 so now the answer is 8 7/12.