Does $\left\lfloor\frac{a}{bv} - \frac{c}{dv}\right\rfloor = \left\lfloor\frac{\left\lfloor\frac{a}{b} - \frac{c}{d}\right\rfloor}{v}\right\rfloor$

Question

Let $a,b,c,d,v$ be positive integers.

Does it follow that:

$$\left\lfloor\frac{a}{bv} - \frac{c}{dv}\right\rfloor = \left\lfloor\frac{\left\lfloor\frac{a}{b} - \frac{c}{d}\right\rfloor}{v}\right\rfloor$$

Answer 1

Put $(a,b,c,d,v) = (3,11,7,17,3)$. Then, left hand side is 1 while right hand side is 0.

Answer 2

No. Let $\frac {a}{b}-\frac {c}{d} = 1.4$ and $v=\frac{1}{3}$. The first expression is equal to 4, and the second one to 3.