So, it would be the wisest to work in decimals for this problem.
[tex] 12\frac{1}{8}=12.125\\
1\frac{13}{16}=1.8125 [/tex]
So we have to divide 12.125 by 1.8125 to see how many times the latter goes into the former.[tex] \frac{12.125}{1.8125}\approx 6.68965517 [/tex]
So, since the problem asks for how many lengths can go in without remainder, our answer would simply be 6.