downsampling - trying to downsample audio

I am trying to downsample from 44100hz to 8000hz, and I am not sure what I am doing wrong here. 44100 / 8000 is 5.5125, so I am getting hung up a little on the fractional remainder which is causing my implementation to play back slightly slower than it is supposed to. It seems that I need to somehow use the fractional remainder to compensate for this, but I am not sure how...

def downsample
  s = low_pass_filtered_signal_by_half_target_sample_rate
  samples_to_discard = (sample_rate.to_f / target_sample_rate).floor //   (44100.0 / 8000.0).floor

  s1_n = 0
  for (n = 0; n < N; n++) {

     if (n % samples_to_discard == 0) {
       s1[s1_n] = averaged(n, samples_to_discard)
       s1_n += 1
    }
  }
end

def averaged(start_index, samples_to_discard)
  sum = 0
    for (n = start_index, n < start_index + samples_to_discard; n++) {

      sum += s[n] || 0
    }
  sum / samples_to_discard
end