There are two important things you need to know and it is very important to keep these in mind to avoid common pitfalls.
First, you cannot add the denominators; you can only add the numerators. Let's illustrate why it does not make sense to add the denominators.
1
2

+
1
2

≠
1 + 1
2 + 2

1
2

+
1
2

≠
1 + 1
2 + 2

1 + 1
2 + 2

=
2
4

1 + 1
2 + 2

=
2
4

However, half + half = 1 (half a pizza + half a pizza = 1 pizza)
1
2

+
1
2
= 1

1
2

+
1
2
= 1

Second, you can only add the numerators when the denominator is the same for both fractions. Since we don't add the denominators, the denominator stays the same.
Having said that, when adding fractions and the denominators are not the same, you need to find equivalent fractions that give a common denominator for both fractions.
Let us illustrate what we just said with examples.
What is the answer for
3
2

+
1
2

Add:
2
3

+
3
6

4
6

is an equivalent fraction for 
2
3

and it has the same denominator as 
3
6

What you are really adding is 
4
6

+
3
6

(Add 4 and 3) The answer is 
7
6

3
5

+
2
4

Multiply the numerator and denominator for 
3
5
by 4

Multiply the numerator and denominator for 
2
4
by 5

You will get 
12
20
+

10
20

3
5
+

2
4

=
3
5

×
4
4

+
2
4

×
5
5

=
12
20

+
10
20

=
22
20

What is the answer for
3
2

+
1
2

Add:
2
3

+
3
6

4
6

is an equivalent fraction for 
2
3

What you are really adding is 
4
6

+
3
6

3
5

+
2
4

You will get 
12
20
+

10
20

3
5
+

2
4

=
3
5

×
4
4

+
2
4

×
5
5

=
12
20

+
10
20

=
22
20

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