Understanding sampling rate conversion I am a little bit confused about the concept of sampling rate conversion. Consider the following question:

Wideband telephony signals are sampled at a sampling frequency fS1 = 16kHz. To process these signals with an automatic speech recognizer, the sampling rate is converted here to fS2 = 11.025kHz, i.e., the wideband signal is ﬁrst upsampled by a factor U, lowpassﬁltered, and ﬁnally downsampled by a factor R. Determine the lowest possible values for R and U.

I am not sure whether U / R = 16kHz / 11.025 kHz, or vice-versa?
You would upsample by 441 and downsample by 640 since $11025 \cdot 640 = 16000 \cdot 441$

That would be a rather expensive operation, so in practice you would either fugde it a bit: 31/45 would get you to 11022Hz and 11/16 to 11000 Hz or you would use a suitable poly-phase irrational conversion algorithm