True
Density = mass/volume
Suppose that a block has a mass of 20 g and a volume of 20 cm^3.
Density = 20 g/20 cm^3 = 1 g/cm^3
Now, you cut the block in half. The half-block has a mass of 10 g and a volume of 10 cm^3.
The density of the half-block is
Density = 10 g/10 cm^3 = 1 g/cm^3
The density <em>stays the same</em>, even though the size of the sample has changed.