Dmitry B. answered • 06/28/20
Five years of Prealgebra tutoring at a math group
The truth is that you don't! The use of the least common denominator is nothing, but just a shortcut. It is perfectly fine to travel from Princeton, NJ to NYC through Atlanta. Why not? We can say the same for adding or subtracting rationals. I can prove this right here:
1/2 + 1/3 = 6/12 + 4/12 = 10/12.
Here, I didn't use LCD (which is 6) and I still got a correct answer of adding 2 rationals. Yes, 10/12 is a correct answer even if it is not a simplified form of the fraction which is 5/6. 10/12 and 5/6 are two different forms of THE SAME number.
Thus, in school they teach you to use LCD because this way you will get a simplified form of the fraction and then you will be able to pass a test (because those who created tests also want this to be written in a simplified form) and so on. As result you are confused because you might think this is the only correct way to deal with fractions, which is not a case as you can see now.
