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 viceversa.
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 aabcddaabcdd, which equals zero. tahdah 
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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