Why must denominators be the same when adding or subtracting fractions?

Answer 1

You have to have like forms to add them or subtract one from the other if the answer is to be a single form quantity. You cannot subtract 2 Oranges from a dozen apples. You first would have to convert the apples to mush, then subtract the equivalent of 2 oranges worth of mush, and then see how much mush you have left. If you added 2 oranges to a dozen apples, you would first convert both to a common form, mush, then add the apple mush and the orange mush to see how much fruit mush you have. Similarly, with fractions, you have to convert them to a common form, referred to as their common denominator, then you can add or subtract to find the result in their common form. If you do not convert the fractions to a common form, or denominator, the resulting answer will look like the original question and not be an answer at all.