Fractions: How Do I Add Thee, Let Me Count the Ways

When it comes to adding fractions, everyone knows that there is only one good way to do it. Right?

So, if I were to ask you to add something simple like 1/2 + 1/4, you would say that we have to find the LCD and change 1/2 into 2/4, add, and get a sum of 3/4. Right?

Or could I change 1/2 into 50% and 1/4 into 25% and then add and get 75% which is equivalent to 3/4? Possibly?

Or could I say that on a clock, 1/2 is the same as 6/12 and 1/4 is the same as 3/12 and then add and get 9/12 which is the same as 3/4? Any chance?

Admittedly, the problem above is very simple. Also, the problem was designed so that three or more methods could be used easily to solve the problem. Not all problems are so friendly! In fact, much of what we do in class centers on finding methods that work for the numbers presented.

Please think about how 1/2 + 1/7 would be different. Do you know both percents? Do you know what 1/7 of a clock face looks like? I don't!