Explanation:
the ratio is
1/2 mile per 3 minutes
= 1/2 / 3
now, we need to keep the value of that ratio unchanged but still transform the ratio (= a fraction) so that we get as ultimate denominator 1 instead of 3 (how far did he run in 1 minute).
what do we need to do to transform 3 to 1 ?
we need to divide by 3.
and because we have to keep the ratio value, we have to devide also the numerator by 3 :
1/2 / 3 × 1/3 / 1/3 = (1/2 × 1/3) / (3 × 1/3) = 1/6 / 1
so, we can read from the result directly :
when running with the same pace (ratio) for 1 minute, he will run 1/6 mile.