OK. You've probably got a raster with 0.1 values for the shapefile area but surrounded by NoData values for the rest of the extent. When you add the 2 rasters together, the NoData wipes out the other raster values.
Ensure NoData values are set to zero in your smaller-area raster using the Recalssify tool, then add them together in raster calculator ensuing that the processing extent is set to union of inputs or another appropriate extent.