How to figure out number of multiplications in rational sampling
That depends a fair bit on how exactly you implement the conversion but if you follow the textbook approach it would probably look like this:

The generic order of sampling rate change is &quot;upsample&quot;, &quot;filter&quot;, &quot;downsample&quot;.
That means that you need to run the filter at the upsampled rate, i.e 5000
Your IIR filter has 9 non-trivial coefficients, i.e. you need to do 9 multiplies per input/output sample
In total that's 9*5000 = 45000 multiplications per second.

That's a lot and that's whey rational sample rate converters often implemented as polyphase FIR filters. Using an IIR requires you to calculate all output samples of the filter although you will be throwing 6 out of 7 away.