in math class we are given fractions like 632/6241 and are expected to know what they reduce to in under 10 seconds.
Currently, I can only guess by trial and error until I find that the common factor is 79. The problem is, much of the time I incorrectly conclude there is no common factor given the time constraint.
What is the best way to quickly reduce fractions with 4 or more digits?
Thanks.
As mentioned in the comments, the Euclidean algorithm is probably the best bet unless someone memorized that $6241 = 79^2$.
One possible way of doing this specific example could be like this: $$ x_1 = 632/6241 \\ 1/x_1 = 6241/632 = (6320 - 79)/632 = 10 - 79/632 = 10 - x_2 \\ 1/x_2 = 632/79 = (790 -158)/79 = 10 - 158/79 = 10-2 = 8 \\ Therefore \\ 1/x_1 = 10 - 1/8 = (80-1)/8 = 79/8 \\ x_1 = 8/79 $$
Though I doubt it is any faster than any other method in general.