i have been stuck on this matter for hours trying to figure it out so i can get ready for intermediate algebra at a local community college's placement test, could anyone help me figure it out?

problem: in a mathmatical problem where i subtract 1 or 2(+) mixed number(s) fraction could i find the LEAST common denominator by following a trail of common denominators before the problem is solved as an attempt to narrow it down to what the least common denominator would be or does finding the least common denominator become an absolute/default (by default i mean cannot be broken down and has only one least common multiplier that works period) must in order to solve the problem?

May 11th 2011, 12:48 PM

emakarov

I am not sure I understand your question. An example would help a lot.

My best guess is that you are asking if you can first add (or subtract) just some, not all, of the fractions by finding their common denominator, or if you have to find the common denominator of all fractions at once. Well, the least common denominator is the least common multiple (LCM) of the denominators, and LCM can be found in any order, just like addition or multiplication. For example, LCM(x,y,z) = LCM(x,LCM(y,z)) = LCM(LCM(x,y),z) (this property is called associativity). Therefore, if you need to add three fractions x' / x + y' / y + z' / z, you can add the first two fractions by finding the LCM of x and y and then add the third one by finding the LCM of LCM(x,y) and z, or you can add the last two fractions first, or you can add all three by finding LCM of x, y and z at the same time.