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November 24th, 2017, 06:28 AM  #1 
Newbie Joined: Nov 2017 From: Portugal Posts: 1 Thanks: 0  Use 0 in rule of 3?
Hello! I'm doing a AHK script. If 0 does nothing, 1 doubles, what do I do with this: (16/9)/0=(14/9)/x? The number 0 in rule of three screws it all. I just want to have 0 as a normal number. I tried changing 0 to 1 and then subtract 1 from x. It gave me 0,125. I don't know if it worked or if it's even correct, so what can I do? 
November 24th, 2017, 07:44 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,151 Thanks: 2390 Math Focus: Mainly analysis and algebra 
You can't divide by zero.

December 1st, 2017, 01:11 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,959 Thanks: 802 
I haven't seen the term "rule of three" in years and then in a very old book! The "rule of three" is an old term for a proportion given any three of a, b, c, or d in $\displaystyle a:b::c:d$ or (in more modern notation) $\displaystyle \frac{a}{b}= \frac{c}{d}$, you can solve for the fourth. $\displaystyle \frac{a}{b}= \frac{c}{d}$ can also be written as $\displaystyle \frac{b}{a}= \frac{d}{c}$, $\displaystyle \frac{a}{c}= \frac{b}{d}$ or even $\displaystyle ad= bc$. As others have said, you cannot divide by 0 so it makes no sense to write "$\displaystyle \frac{16/9}{0}= \frac{14/9}{x}$" but that can be written as $\displaystyle \frac{0}{16/9}= \frac{x}{14/9}$ which reduces very quickly to x= 0. In fact, in order for "$\displaystyle \frac{A}{0}= \frac{B}{x}$" to make sense, for any A, B, we must have x= 0. 

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