[ $\left[\begin{array}{ll}\text { Irreducible fractions }\end{array}\right]$

What number should be subtracted from the numerator of the fraction ${ }^{537} / 463$ and added to the denominator to obtain $1 / 9$ after simplification?
Notice that $537+463=1000$.

## Solution

The sum of the numerator and the denominator will not change if the same number is subtracted from one and added to the other. Since this sum is 1000, the fraction before simplification should be $100 / 900$, and to obtain it, the number 437 must be subtracted from one and added to the other.

## Answer

437.