www.mikescher.com/www/statics/euler/Euler_Problem-071_explanation.md

For every denominator from 1 to 1 000 000 we generate a possible fraction where the numerator is (d * 3) / 7. (Every other fraction is either greater than 3/7 or has a greater difference than the generated).

Now everything thats left is finding the fraction with the smallest difference to 3/7.

The difference of two fractions is calculated (without floating points) by:

n1/d1 - n2/d2  ==  (n1*d2 - n2*d1)/(d1*d2)

The rest is just iterating through all the possible fractions and in each step remembering the current best.

We don't even need to reduce the result to get a proper fraction. If it could be reduced we would have got the reduced version first. (Because it has an smaller denominator).