SOLUTION: this is a complex fraction that I have attempted to solve but I am unable. Please help. 3over 4 + 2 over 5 long line which means divide I think 1 over 2 +3 over 5

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Question 215851: this is a complex fraction that I have attempted to solve but I am unable. Please help. 3over 4 + 2 over 5 long line which means divide I think 1 over 2 +3 over 5
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
%28%283%2F4%29+%2B+%282%2F5%29%29%2F%28%281%2F2%29+%2B%283%2F5%29%29

There are two main methods of simplifying this. A lot of books call it "Method I" compared to "Method II." Probably the best way to explain it here is called "Method I". I call this the "un-stacking method."

The longer line means "DIVIDE", so just "un-stack the problem like this:

%28%283%2F4%29+%2B+%282%2F5%29%29 DIVIDED BY %28%281%2F2%29+%2B%283%2F5%29%29

Next, you have to simplify each fraction by finding a common denominator for each. The LCD for the first fraction is 20. The second is 10. Write it like this:

%28%283%2F4%29+%2B+%282%2F5%29%29 DIVIDED BY %28%281%2F2%29+%2B%283%2F5%29%29
%28%283%2F4%29%2A%285%2F5%29+%2B+%282%2F5%29%2A%284%2F4%29%29 DIVIDED BY %28%281%2F2%29%2A%285%2F5%29+%2B%283%2F5%29%2A%282%2F2%29%29


%28%2815%2F20%29+%2B+%288%2F20%29%29 DIVIDED BY %28%285%2F10%29+%2B%286%2F10%29%29
%2823%2F20%29+ DIVIDED BY %2811%2F10%29+

Now, invert the second fraction and multiply:
%2823%2F20%29%2A%2810%2F11%29+

Divide out the 10:

%2823%2F2%29%2A%281%2F11%29+
23%2F22

I have a pretty good page about complex fractions if you need to this with variables like x and y. If you need to see this, then find my homepage by doing a Google search for my last name "Rapalje". Look for the "MATH IN LIVING COLOR" page near the top of my Homepage. Choose "Intermediate Algebra", and look in Chapter 2 for the topic "Complex Fractions."

R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus