0

Suppose $a,b,c,d$ to be whatever quantities whatsoever that satisfy the proportion $\frac{a}{b}=\frac{c}{d}$. Is there a value for $a$ other than a factor or a multiple of $c$. Or, is there a value for $b$ other than a factor or a multiple of $d$.

I am sure there cannot be such a value but at the same time there is no way for me to prove it.

  • Take for example $a=b=35,c=d=66$ – kingW3 Feb 16 '15 at 09:00
  • @kingW3 That's true but that's a very special case where the 2 fractions aren't really two fractions but simply 2 real numbers. –  Feb 16 '15 at 09:04
  • 2
    4/6 = 6/9 4 is not a factor or multiple of 6. 6 is not a factor or multiple of 9. Instead of "factor or multiple", do you mean "relatively prime"? – Peter Webb Feb 16 '15 at 09:07
  • @PeterWebb But those two fractions can be simplified down to $2/3$. Yes, what I mean is what about relatively prime fractions ? Where the numerator and the denominator have no factors other than 1 ? –  Feb 16 '15 at 09:28

1 Answers1

0

The given expression is ad=bc if a and b are two different numbers such that their greatest common factor is 1

Case-1: If Z is least common multiple of a and c, b=z/c and d=z/a clearly satisfies the equation. ( you may change the variables)

Case-2: If cd=ad=0 then c may or may not be equal to a

Case-3: if above are not the cases then they has to be surely equal.

Sherlock
  • 1