When adding 5/14 + 5/21, can you just add the bottom numbers together since the top is the same?

The bottom line must be the same.
15/42 + 10/42 = 25/42

No the addition or subtraction of fractions can only be done when the denominators are the same. Therefore, you must convert them to a common one first.

Since 14 = 2*7 and 21 = 3*7

the common denominator is 2*3*7 = 42

Multiply 5/14 top and bottom by 3 to get

15/42

Multiply 5/21 top and bottom by 2 to get

10/42

The expression is then

15/42 + 10/42 = (15+10)/42 = 25/42

No, you have to find a common denominator. 5/14 =15/42 and 5/21 = 10/42

15/42 + 10/42 = 25/42

5/14 + 5/21
= (5 x 3)/(14 x 3) + (5 x 2)/(21 x 2)
= 15/42 + 10/42 (42 is the least common denominator)
= 25/42

It only applies when denominator is same.
In this case you need to take LCM of denominator.

No. You can only add the top numbers when the bottom numbers are the same.

Only applies when the denominator is the same.

Things have to be divided into the same number of pieces - think of a Trivial Pursuit game piece.

5/14 = 15/42
5/21 = 10/42

Adding, we get 25/42

it only applies when the denominator is the same!!!