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 December 8th, 2014, 08:02 AM #1 Newbie   Joined: Mar 2013 Posts: 9 Thanks: 0 algebra to invert fractional equation? so.. if a/b=c/d then b/a=d/c because you can use each side of the equation do divide one by to invert. how do i represent this as an explicit step in place of just flipping the fractions? would a/b=c/d 1/(a/b)=1/(c/d) b/a=d/c be legit algebra? this seems wrong somehow. December 8th, 2014, 08:18 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,155 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions Yep. Doing "1 over" is a valid mathematics operation on both sides of an equation provided you don't have any zeroes. It's okay to do $\displaystyle x = -y$ $\displaystyle \frac{1}{x} = -\frac{1}{y}$ (if x and y are non-zero), but not $\displaystyle x+y = 0$ $\displaystyle \frac{1}{x+y} = \frac{1}{0}$ because 1 divided by 0 is undefined. Also, you need to pay attention to the fact that in the first case presented above, x and y must be non-zero. Otherwise you're doing the same thing as the second case. As for your specific example, another way of showing that they are the same is to multiply both sides by $\displaystyle \frac{bd}{ac}$ $\displaystyle \frac{a}{b} = \frac{c}{d}$ $\displaystyle \frac{a}{b} \times \frac{bd}{ac}= \frac{c}{d} \times \frac{bd}{ac}$ $\displaystyle \frac{\cancel{a}}{\cancel{b}} \times \frac{\cancel{b}d}{\cancel{a}c}= \frac{\cancel{c}}{\cancel{d}} \times \frac{b\cancel{d}}{a\cancel{c}}$ $\displaystyle \frac{d}{c} = \frac{b}{a}$ which is okay if a, b, c and d are non-zero. December 8th, 2014, 10:32 AM #3 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 Another way of simplifying 1/(a/b) with a*b is nonzero, is as follows: $\displaystyle \frac{1}{\frac{a}{b}} = \frac{1}{\frac{a}{b}} \cdot 1 = \frac{1}{\frac{a}{b}} \cdot \frac{b}{b} = \frac{b}{\frac{a}{b} \cdot b} = \frac{b}{\frac{ab}{b}} = \frac{b}{ \frac{b}{b} \cdot a} = \frac{b}{1 \cdot a} = \frac{b}{a}$ where you might like to leave out some steps. Tags algebra, equation, fractional, invert Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post watkd Algebra 1 July 26th, 2012 06:00 PM hampos Real Analysis 3 May 27th, 2012 12:44 PM pyth0n Algebra 1 October 27th, 2011 07:59 PM squerlyq Algebra 5 December 5th, 2008 05:14 AM Gerald79 Algebra 4 March 25th, 2008 08:43 PM

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