linguistic:translation
Interval for a convergent

A rational number, which can be expressed as finite continued fraction in two ways,

will be one of the convergents for the continued fraction expansion of a number, if and only if the number is strictly between (see this proof)

The numbers x and y are formed by incrementing the last coefficient in the two representations for z. It is the case that x < y when k is even, and x > y when k is odd.

For example, the number 355 / 113 has the continued fraction representations

and thus 355 / 113 is a convergent of any number strictly between