Next | Continued Fraction Arithmetic | 23 |

How the heck do you do arithmetic on continued fractions?

How do you add, subtract, multiply and divide them?

Or consider this:

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]

It seems that the only way to evaluate this is to turn both addends into rational numbers

Which defeats the whole purpose

And anyway doesn't work for infinite continued fractions

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