According to the principle of homogeneity of dimensions, only physical quantities with the same dimensions can be added or subtracted . Therefore, if A and B have different dimensions, the operations $A + B$ and $A - B$ are physically meaningless . However, physical quantities with different dimensions can be multiplied or divided to result in a new derived quantity . For example, dividing distance (length) by time results in velocity . Thus, the operation $A/B$ is physically meaningful.