 Thus, the first two equations may be combined to form

The third equation may be used to substitute the denominator term "r"1/"r"0, yielding

The final ratio of remainders "r""k"/"r""k"−1 can always be replaced using the next equation in the series, up to the final equation.The result is a continued fraction

In the worked example above, the gcd(1071, 462) was calculated, and the quotients "q""k" were 2, 3 and 7, respectively.Therefore, the fraction 1071/462 may be written

as can be confirmed by calculation.