(Abridged) We use 8 micron Spitzer GLIMPSE images to make extinction maps of 10 IRDCs, selected to be relatively nearby and massive. The extinction mapping technique requires modeling the IR background intensity behind the cloud, which is achieved by correcting for foreground emission and then interpolating from the surrounding regions. The correction for foreground emission can be quite large, thus restricting the utility of this technique to relatively nearby clouds. We investigate three methods for the interpolation, finding systematic differences at about the 10% level, which, for fiducial dust models, corresponds to a mass surface density Sigma = 0.013 g cm^-2, above which we conclude this extinction mapping technique attains validity. We examine the probability distribution function of Sigma in IRDCs. From a qualitative comparison with numerical simulations of astrophysical turbulence, many clouds appear to have relatively narrow distributions suggesting relatively low (<5) Mach numbers and/or dynamically strong magnetic fields. Given cloud kinematic distances, we derive cloud masses. Rathborne, Jackson & Simon identified cores within the clouds and measured their masses via mm dust emission. For 43 cores, we compare these mass estimates with those derived from our extinction mapping, finding good agreement: typically factors of <~2 difference for individual cores and an average systematic offset of <~10% for the adopted fiducial assumptions of each method. We find tentative evidence for a systematic variation of these mass ratios as a function of core density, which is consistent with models of ice mantle formation on dust grains and subsequent grain growth by coagulation, and/or with a temperature decrease in the densest cores.
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