SOLUTION: 1/3y+1/6y divided 1/2y+3/4y

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Question 388555: 1/3y+1/6y divided 1/2y+3/4y
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F3y%2B1%2F6y%29%2F%281%2F2y%2B3%2F4y%29
A way I like to do these problems is to
  1. Find the least common denominator of all the "little" fractions.
  2. Multiply the numerator and denominator of the "big" fraction by the least common denominator of the "little" fractions.

Done correctly this will eliminate all the "little" fractions. In your expression the "little" denominators are 3y, 6y, 2y and 4y. The least common denominator of these is 12y. So we will multiply the numerator and denominator of the "big" fraction by 12y:
%28%281%2F3y%2B1%2F6y%29%2F%281%2F2y%2B3%2F4y%29%29%2812y%2F12y%29
To multiply the numerators and denominators correctly we will need the Distributive Property:

All the y's cancel. And one of the factors of 12 will cancel with the numbers in the denominators of the "little" fractions giving us:
%284+%2B+2%29%2F%286+%2B+3%2A3%29
which simplifies as follows:
6%2F%286%2B9%29
6%2F15
2%2F5