multiplying things

Physical items have units (aka dimensions)--in many cases they are combinations of dimensions, like pressure (lb/in^2), area (ft^2), density (lb/ft^3). Oranges are a dimensional unit and apples are another dimensional unit, if you create a new dimensional unit like pieces of fruit, then adding apples and oranges makes sense--I have 5 oranges and 7 apples, How any pieces of fruit do I have? Ans 12 pieces of fruit.

Most common dimensional units are combinations of basic, fundamental units--the most common being mass, length, and time--theses usually are English (foot, pound, second) or metric (meter, kilogram, second).

As a rule when dealing with measurements of things, include the units (aka dimensions), and in calculations treat the units algebraically..

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fundamenal units http://en.wikipedia.org/wiki/Fundamental_unit

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