# How do you call the relation between these 2 variables?

Let's say I have an X number and I want to increment it by 50%, I would get

$X*A=Y$

Then in order to multiply Y and get X again I would need to do

$Y*Z=X$

How do you call the relation between A and Z?

Example with numbers:

$$5*1.5=7.5$$ $$7.5*Z=5$$ $$Z=0.66$$

How do you call the relation between 1.5 and 0.66 when $X*1.5*0.66=X$?

A and Z are multiplicative inverses; i.e., A × Z = 1.

Therefore, X × A × Z = X

Usually, we just say that A is the inverse of Z (and vice-versa).

• I prefer 'reciprocal' to just 'inverse', but 'multiplicative inverse' is the most specific and least ambiguous.
– starrise
Feb 26, 2016 at 0:55
• Thanks! What's the difference between both definitions?
– Fraaaan
Feb 26, 2016 at 1:06
• In my experience (BS in math from a US institution) 'reciprocal' and 'multiplicative inverse' are more-or-less equivalent. The term 'inverse' by itself, without the word 'multiplicative' attached, carries a lot of mathematical baggage in that it is used for many different things. Function inverses, inverses of binary operators (addition, multiplication, Fourier transform, etc), inverse mappings, etc. Hence why I prefer 'reciprocal' or 'multiplicative inverse' as they are unambiguous and don't require context to understand.
– starrise
Feb 26, 2016 at 1:31
• @Fraaaan: There are many kinds of inverses: matrix inverse, trigonometric inverse (for example arcsine is the trigonometric inverse of sine but is not defined as 1/sine) etc. But generally reciprocal refers to multiplicative inverse. However, note that in some fields like engineering and physics there could also be many different concepts that have the name reciprocal Feb 26, 2016 at 4:39