SOLUTION: Simplify complex fraction 1/2 +1/3 divided by 1-1/6

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Question 363626: Simplify complex fraction
1/2 +1/3 divided by 1-1/6
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2+%2B1%2F3%29%2F%281-1%2F6%29
This simplest way to simplify a complex fraction, IMHO, is to
  1. Find the Lowest Common Denominator (LCD) of all the denominators of the "little" fractions
  2. Multiply the numerator and denominator of the "big" fraction by the LCD found in step #1.

Let's see how this works on your complex fractions. The "little" fractions are 1/2, 1/3 and 1/6. The LCD of 2, 3 and 6 is 6. So we will multiply the numerator and denominator of the "big" fraction by 6:
%28%281%2F2+%2B1%2F3%29%2F%281-1%2F6%29%29%286%2F6%29
To multiply correctly we will need to use the Distributive Property in both the numerator and denominator:
%28%281%2F2+%2B1%2F3%29%2A6%29%2F%28%281-1%2F6%29%2A6%29%29
%28%281%2F2%29%2A6+%2B+%281%2F3%29%2A6%29%2F%281%2A6+-+%281%2F6%29%2A6%29
%283+%2B+2%29%2F%286+-+1%29
Notice how all the "little" fractions disappear when you multiply by the LCD!
5%2F5
which simplifies to 1!