The fallacy of division is the reverse of the fallacy of composition. It is committed by inferences from the fact that a whole has a property to the conclusion that a part of the whole also has that property. Like the fallacy of composition, this is only a fallacy for some properties; for others, it is a legitimate form of inference.
Example
An example of an inference that certainly does commit the fallacy of division is this:
(1) Water is liquid.
Therefore:
(2) H2O molecules are liquid.
This argument, in attributing a macro-property of water, liquidity, to its constituent parts, commits the fallacy of division. Though water is liquid, individual molecules are not.
Note, however, that an argument with the same logical form but inferring from the fact that a computer is smaller than a car that every part of the computer is smaller than a car would not be fallacious; arguments with this logical form need not be problematic.