Thinking tools is a regular feature that offers tips and pointers on thinking clearly and rigorously.
The fallacy of division involves concluding that if something has a property, then the parts or individuals that go to make it up must have that property.
Some examples:
The cup is white; therefore, the atoms that go to make it up are white.
London is large; therefore, my house in London is large.
Sometimes, what is true of something must then also be true of certain parts or individuals that go to make it up. For example, if my body is made out of atoms, then my legs are made of atoms. But this is not always the case.
The point is that it cannot be assumed that what is true of the whole must be true of the parts.