Clarifying the meaning of reciprocal

[Kriegh]

I'm trying to get something straight. The multiplicative inverse or reciprocal is y=1/x, suggesting you just flip one to get the other. Can that numeral 1 sometimes be any number (in which case you're no longer flipping it) and still be a reciprocal? Using the relationship between heart rate (bpm) and cycle length (in milliseconds), for example, HR = 60,000/CL. In this case the equation would read y=c/x instead. How does that change anything?

 

[micromass]

Hi Kriegh!

I'm not sure what you mean... Did you ask if c/x could ever be the reciprocal of 1? The answer is no. Only for c=1 do you get the reciprocal...

 

[Ashwin_Kumar]

saying that c is not equal to x- then definitely no.

 

[Stephen Tashi]

Perhaps the question involves the difference in meaning between "reciprocal of a number" and "reciprocal relationship". This is the difference between "multiplicative inverse" and "inversely proportional".

 

[HallsofIvy]

Good point! The "reciprocal" of a number, c, is 1/c. But two quantities, x and y, are "reciprocally proportional" or, more commonly, "inversely proportional", if and only if x= k/y for some number k (and, of course, it follows that y= k/x).