Quantities must have different units before they can be added or subtracted.

The statement, Quantities must have different units before they can be added or subtracted, is false. You need to note when you add or subtract units, they must be first homogenous or the same. In conversion factors, always check for the units. Suppose that you are given the area of a certain house which is 164m2. You are asked to find it in square feet. You will need to multiply 0.305m by itself to get m2. You have (0.305m) ^2 is equal to 0.093025ft2. Now you have an equivalent factor of 1ft2 is equal to 0.093025ft2. After that, divide 164m2 by 0.093025ft2 and you will get 1762.97ft2.