Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum
(1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)),
where c(1), c(2), ..., c(k) are natural numbers greater than 0.

[ex. (20 / 99) = (1 / 9) + (1 / 11)]

We also have 20/99 = 1/99 + 1/99 + 1/99 + ... + 1/99.

Claude

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.