Explanation:
if the goal is to have both numbers with denominator 6, then the first one is totally simple :
3 1/6 = 3 1/6
what else could it be ... ?
and the second, well, how many thirds are in a whole ?
right, 3, that's why we call them "thirds".
how many 6ths are in a whole ?
right, 6.
do you notice something ? it is easy to get from 3 to 6 by multiplying 3 by 2.
in order to keep the overall value of a fraction unchanged, when we multiply one part of the fraction by something we need to multiply the other part by the same number too.
so,
5 2/3 = 5 2/2×2/3 = 5 4/6
in short : yes, every third contains 2 6ths.
therefore, 2/3 = 4/6