What fraction is all about?

I never know that fraction could arise so many questions in our head. Yesterday it was a hot topic discussed by my MATHS302 classmates and I really enjoyed their conversation. Actually I was mesmerized. How this small topic could arise so many questions in many different aspects.
For example, how would you explain to a kid that 1/2 + 2/7 is actually 11/14 and not 3/9 which is the most common answer you would find. What kind of explanation I would give that would give if not perfect maybe almost perfect explanation to kids who are eagerly waiting for the answer? All I know is we should first and for most equalize the denominator which in this case is 14. And that is what I told my teammates. And obviously there is a disagreement there. We should explain them how, give some sense to it? Emm now my mind starting to think; how?
What of the class member throw a simple idea but totally understandable. Lets cut two equal size of paper; one of them make it into two and the other one divided by seven. Then just simply show that the half of paper + 2 parts of 7 is simply bigger that 1/3. Emm that sounds good to me. Nothing like you need to multiply 2 by 7 first and then carry out with addition blah blah blah. When you switch on their understanding switch, then their curiosity level will increase and it will be easier for the to digest what you deliver.
Wow, that is the right way of teaching. Not operation understanding that should be cultivate, but the understanding about what fraction actually is. Cause if the teacher taught them what they should do, they will never understanding what fraction is about. If fraction which only the basic concept the children hardly understand, then how they will carry on higher level of mathematics? What a big challenge for the teachers to handle. Lots of thing need to be taken into account. And Insya Allah one day I will need to think about all those aspects as well.