Intuitively, why does a c = 1 c a ?For intuition, I reference objects. Imagine making a dessert with: a as apples and c as chestnuts.Question. How and why is a c ( 3 ) = 1 c a ( 4 ) ?I ask only about intuition; please omit formal arguments and proofs (eg: Intuition is not generated by the explanation that rationalising (4)'s denominator produces (3)).

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Intuitively, why does             a      c        =            1              c        a            ?For intuition, I reference objects. Imagine making a dessert with:   a as apples and   c as chestnuts.Question. How and why is            a      c          (  3  )    =                      1                              c          a                        (  4  )    ?I ask only about intuition; please omit formal arguments and proofs (eg: Intuition is not generated by the explanation that rationalising (4)&#039;s denominator produces (3)).

alisonhleel3 · Accepted Answer

The fraction       a    c   is the number of apples per chestnut, and       c    a   is the number of chestnuts per apple.Suppose that you have   x chestnuts per apple, where   x can be any positive real number. No matter what   x is, each one of those   x chestnuts must be getting       1    x   of an apple, so there are       1    x   apples per chestnut.Thus, in the particular case that   x  =      c    a  , it must be the case that      a    c    =      1          c      a          .

Celia Lucas · Accepted Answer

I think the best way to think about this is as a nested fraction. Let&#039;s let   k  =  c      /    a.Your number is  a      /    c  =  1      /    (  c      /    a  )  =  1      /    k  =  1      /    chestnuts per appleIntuitively, you can think about this in one of two ways as:the flip (i.e. Inverse) of the thing on the bottom (making it the number of apples per chestnut) oryou have one apple and you can feed people at a rate of   k chestnuts per apple, and so if you have to feed   1 chestnut, how much of an apple do you need? Reminder that the equation is for feeding people is   c  =  k  a

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