A Compounding Question.
Math brain teasers require computations to solve.
Simplify the following expression:
(a/b) / (c/d) - (d/c) / (b/a)
Comments
thebuddhawithin 
Jul 04, 2004
| I don't get it |
canu
Jul 13, 2004
| The typographical presentation is a bit confusing.
--- It is the difference between two fractions.
--- The first fraction is (a/b) / (c/d). It is equal to (a/b) x (d/c) = ad/bc
--- The second fraction is (d/c) / (b/a). It is equal to (d/c) x (a/b) = da/cb
|
alleycat1226
Mar 13, 2005
| my head hurts lol  |
musicmaker21113
Jan 10, 2006
| To solve it:
(a/b)/(c/d) - (d/c)/(b/a)
This represents the difference of two fractions with different denominators. In order to subtract the two fractions, you need to come up with a common denominator. The easiest way is to multiply and divide the first fraction by the denominator of the second, and vice-versa.
Like this: 3/4 - 2/5
(5/5)*(3/4) - (4/4)*(2/5)
(15/20) - (8/20) = 7/20
It's perfectly fine to multiply a fraction by a number over itself, as this is the same thing as multiplying by 1 (i.e. 5/5 = 1, so (5/5)*(3/4) = 1*(3/4) = 3/4.)
So, to solve this problem:
(a/b)/(c/d) - (d/c)/(b/a)
or
(a/b) (d/c)
------ - -----
(c/d) (b/a)
(b/a)*(a/b) (c/d)*(d/c)
------------- - -------------
(b/a)*(c/d) (c/d)*(b/a)
The numerators here both multiply to one, since multiplying reciprocal fractions always equals 1:
(b/a)*(a/b) = 1 and
(c/d)*(d/c) = 1, so the above equation now is:
1 1
---------- - -----------
(b/a)*(c/d) (c/d)*(b/a)
Since the order in which you multiply two numbers is interchangable, this is also:
1 1
---------- - -----------
(b/a)*(c/d) (b/a)*(c/d)
since you are subtracting the same fraction from itself, the answer must be zero.
Clear as mud, right?!?
  |
musicmaker21113
Jan 10, 2006
| Argh, the spacing of the 1's was put too close together... Oh well, I tried! |
keveffect1  
Feb 27, 2006
| why is there an open calculator you can get the answer just by looking at it |
MadDog72
Mar 12, 2006
| I think the "Open Calculator" button appears for any problem labeled "Math". Also, this problem says "Solve the equation", but there is no equation. It should read, "Simplify the expression." |
Crazycriely
Apr 08, 2006
| well...ummm...i knew the answer was 0 but i dont know how |
stil
Apr 23, 2006
| How about common fraction? With everything expressed as divided by abcd (the product a*b*c*d), the numerator is (aacd/abcc)-(abdd/bbcd). With its common divisor as abbccd, the its numerator becomes aabcdd-aabcdd, which equals zero. tah-dah |
banzai
Jul 14, 2006
| this was extremely easy for me. First for everything! thank you for making me feel smart. |
GebbieRose
Aug 12, 2006
| Simple. Just follow the order of operations!  |
javaguru
Feb 03, 2009
| I did it the same as Canu.
I think Musicmaker made the problem about as difficult as possible.  |
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