Recent observational evidence suggests that the coarse angular resolution ($sim20$ FWHM) of single-dish telescopes at sub-mm wavelengths has biased the observed galaxy number counts by blending together the sub-mm emission from multiple sub-mm galaxies (SMGs). We use lightcones computed from an updated implementation of the galform semi-analytic model to generate $50$ mock sub-mm surveys of $0.5$ deg$^2$ at $850$ $mu$m, taking into account the effects of the finite single-dish beam in a more accurate way than has been done previously. We find that blending of SMGs does lead to an enhancement of source extracted number counts at bright fluxes ($S_{mathrm{850}mumathrm{m}}gtrsim1$ mJy). Typically, $sim3{-}6$ galaxies contribute $90%$ of the flux of an $S_{850mumathrm{m}}=5$ mJy source and these blended galaxies are physically unassociated. We find that field-to-field variations are comparable to Poisson fluctuations for our $S_{850mumathrm{m}}>5$ mJy SMG population, which has a median redshift $z_{50}=2.0$, but are greater than Poisson for the $S_{850mumathrm{m}}>1$ mJy population ($z_{50}=2.8$). In a detailed comparison to a recent interferometric survey targeted at single-dish detected sources, we reproduce the difference between single-dish and interferometer number counts and find a median redshift ($z_{50}=2.5$) in excellent agreement with the observed value ($z_{50}=2.5pm 0.2$). We also present predictions for single-dish survey number counts at $450$ and $1100$ $mu$m, which show good agreement with observational data.
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