# How to figure out number of multiplications in rational sampling

I am trying to understand the following:

Consider a system implementing a rational sampling rate change by $$\frac{5}{7}$$: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency $$\frac{\pi}{7}$$ and a downsampler by 7. The lowpass filter is a 4th order Butterworth filter with transfer function

$$H(z) = \frac{b_0 + b_1 z^{-1} + b_2 z^{-2} + b_3 z^{-3} + b_4 z^{-4}}{1 - a_1 z^{-1} - a_2 z^{-2} - a_3 z^{-3} - a_4 z^{-4}}$$

Assume that the input works at a rate of 1000 samples per second. What is the number of multiplications per second required by the system? Assume that multiplications by zero do not count and round the number of operations to the nearest integer.

I would like to know how to approach this problem and get a general idea. I am taking an online course on my own and there is very little reference material, so I was trying to figure out a good way to approach this problem, but I am stuck with the logic behind it.