Mean total precipitation rate vs sum of large scale and convective precipitation rates


As per the definition of the 'mean total precipitation rate', it is calculated as sum of the rates due to large-scale precipitation and convective precipitation. However, when I calculated the sum of convective rain rate, mean convective snowfall rate, large scale rain rate and large scale snowfall rate over a grid for the same time step, the sum was different (1.29 vs 1.26; slight difference) from the 'mean total precipitation rate'. Could someone please help me understand what is causing this difference  to appear?