Next | Continued Fraction Arithmetic | 44 |

Like decimals, continued fractions are easy to compare!

Recall:

Is 100/89 more or less than 244/217?

100/89 = [1; 8, 11]

244/217 = [1; 8, 27]

Since the 1/... parts are <1, we can resolve this immediately if

*a*_{0}≠*b*_{0}Otherwise, the answer is the same as:

Which is just:

Summary: compare place by place until you find a mismatch

If the first mismatch is in an even position, invert the sense of the result

0 = [0] 1/8 = [0; 8] 2/8 = [0; 4] 3/8 = [0; 2, 1, 2] 4/8 = [0; 2] 5/8 = [0; 1, 1, 1, 2] 6/8 = [0; 1, 3] 7/8 = [0; 1, 7] 1 = [1]

If one fraction ends prematurely, that's just like encountering

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