Question

A segment of lenght 3 is made up of how many segments of length 3/5?

Answer 1

namely, how many times does ⅗ go into 3?  well, is just their quotient.

$\bf 6\div \cfrac{3}{5}\implies \cfrac{6}{1}\div \cfrac{3}{5}\implies \cfrac{6}{1}\cdot \cfrac{5}{3}\implies \cfrac{6}{3}\cdot \cfrac{5}{1}\implies 2\cdot \cfrac{5}{1}\implies 10$

Answer 2

To answer this, divide 3 by 3/5.  To do that, invert the divisor, obtaining 3(5/3), and then multiply.  The 3's cancel out, so we are left with 5.  5 segmens of length 3/5 can be obtained from one segment of length 3.