No that wouldn't work. e.g 1/2 + 1/2 would become 2/4 (which is equivalent to 1/2) if you just added the numbers, which can't be right.
You need to find equivalent fractions so that each fraction has the same number on the bottom (denominator) and then add ( or take away) the top numbers.
1/2 + 1/2 has same number on bottom, so just add top numbers to get 2/2 =1
so 1/4 + 1/2 has diff nos on bottom, so change 1/2 to 2/4. 1/4 + 2/4 = 3/4
2/3 - 1/4 = 8/12 - 3/12 = 5/12
You may need to ask your teacher about equivalent fractions.