A physicist wants to compute the density of an object, defined as mass divided by volume. Which expression could represent a valid…

Density is defined as mass per unit volume, which is mass divided by volume. With $m$ in kilograms and $V$ in cubic meters, the quotient $\frac{m}{V}$ has units of kilograms per cubic meter, choice A. Choice B ($mV$) is a product, which would represent something like mass times volume, not a rate. Choice C ($\frac{V}{m}$) is the reciprocal of density, called specific volume, and has units of cubic meters per kilogram. Choice D ($m + V$) adds quantities with different units, which is not meaningful because you cannot add kilograms to cubic meters. The units confirm the operation.