I am learning some basic DSP and I have a pretty good intuition as to why sampling creates spectral images of the frequency response at intervals of the sampling frequency (convolution with pulse train).

I am reading about sample rate conversions (downsampling/decimation and upsampling/interpolation) and I can't seem to get intuition as to why downsampling/decimation stretches the frequency response by M (the downsample factor) or why upsampling/interpolation compresses it by I (the upsample factor) and creates more images of the originally sampled datas frequency response