Simplifying complex fractions - help please

It's a bit tough to read.

Have you tried finding common denominators for the numerator and denominator?
 
I am new to this site and I am not quite sure how to show the formulas where they are readable.

I came up with 45 as the LCD and with this got an ans of -23 over 27; however, it just doesn't seem right.
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Thank you.

Eliz.
 
Tex148 said:
2 - 2 - 1
5 9 3
1 + 1 + 2
3 5 15
Click to expand...

if that's [2/5 - 2/9 - 1/3] / [1/3 + 1/5 + 2/15],
then your answer should be -7/30: YOU figure out why :twisted:
 
Tex148 said:
I am new to this site and I am not quite sure how to show the formulas where they are readable.

I came up with 45 as the LCD and with this got an ans of -23 over 27; however, it just doesn't seem right.
Click to expand...
I've always been curous about "doesn't seem right". What an odd thing to say. :) Why not? Did you do it correctly? Were there any steps about which you were not confident?

Good job on the 45. Multiply numerator and denominator by 45 and see what comes out. How did you do it before?
 
Hmmm...I do these by not necessarily same LCD for numerator and denominator;
like, for this one, I use 45 for numerator and 15 for denominator:
is there a "teacher rule" that prevents this easier way ? :wink:
 
You can do this sort of thing (assuming I'm interpreting it correctly) either of two different ways. Assuming we have:


. . . . .\(\displaystyle \large{\frac{\frac{2}{5}\,-\,\frac{2}{9}\,-\,\frac{1}{3}} {\frac{1}{3}\,+\,\frac{1}{5}\,+\,\frac{2}{15}}}\)


...you can (1) convert the numerator and denominator to their (possibly different) common denominators, combine, and flip-n-multiply:


. . . . .\(\displaystyle \large{\frac{\frac{2}{5}\,-\,\frac{2}{9}\,-\,\frac{1}{3}} {\frac{1}{3}\,+\,\frac{1}{5}\,+\,\frac{2}{15}}\,= \,\frac{\left(\frac{18\,-\,10\,-\,15}{45}\right)} {\left(\frac{5\,+\,3\,+\,2}{15}\right)}\,= \,\left(\frac{-7}{45}\right)\,\left(\frac{15}{10}\right)\,=\,-\frac{7}{30}}\)


....or else you can (2) multiply top and bottom by the overall common denominator, and simplify:



. . . . .\(\displaystyle \large{\frac{\frac{2}{5}\,-\,\frac{2}{9}\,-\,\frac{1}{3}} {\frac{1}{3}\,+\,\frac{1}{5}\,+\,\frac{2}{15}}\,= \,\left(\frac{\frac{2}{5}\,-\,\frac{2}{9}\,-\,\frac{1}{3}} {\frac{1}{3}\,+\,\frac{1}{5}\,+\,\frac{2}{15}}\right)\.\left(\frac{\frac{45}{1}}{\frac{45}{1}}\right)\, =\,\frac{18\,-\,10\,-\,15}{15\,+\,9\,+\,6}\,= \,-\frac{7}{30}}\)


You'll get the same answer either way, but many students have a strong preference regarding the method they use.

Eliz.
 
Denis said:
Hmmm...I do these by not necessarily same LCD for numerator and denominator;
like, for this one, I use 45 for numerator and 15 for denominator:
is there a "teacher rule" that prevents this easier way ? :wink:
Click to expand...
I don't really see a difference. You choose between reducing the fraction later or dealing with two denominators. Horse-a-piece.
 
Thanks to everyone who helped me with this problem. I discovered I had left out a step.
 
Off-topic, so please pardon, but:

tkhunny said:
Horse-a-piece.
Click to expand...
I've never heard this expression before. Is it like "six of one, a half-dozen of the other"?

Thanks! :D

Eliz.
 
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