(11C) Arithmetic with Fractions

[Albert Chan]

Just want to clarify, Kahan's algorithm basically mechanized below steps:

G = gcd(12345648, 6357263) = 181

M/N = 1234567/12345648 - 635720/6357263
= (6820 G + 147) / (68208 G) - (3512 G + 48) / (35123 G)
= (35123 G *(6820 G + 147) - 68208 G *(3512 G + 48)) / (68208 * 35123 * G^2)
= ((6820*35123 - 3512*68208) G + (147*35123 - 68208*48)) / (68208 * 35123 * G)
= (-7636 G + 1889097) / (68208 * 35123 * G)
= (-7636 G + 10437 G) / (68208 * 35123 * G)
= 2,801 / 2,395,669,584