Expert: Josh - 3/23/2004

Question
Hello:

Why do you believe it is a bad idea to mix units with equal signs?

From your last answer you indicated the following: "Best to avoid mixing units with equal signs, it's a bad idea."

I thank you for your reply.

-----------------------
Followup To
Question -
Hello:

A three-foot wide shelf is used to hold a set of notebooks.  Each notebook has a 3/4 inch wide binding.
How many notebooks can fit on the shelf?

My question pertains to how to express the calculation so that the "inch" units cancel and the answer appears as 48 notebooks not just 48.

3 feet = 36 inches
36 inches divided by 3/4 inches = 48

Where does the "notebook" unit belong in this calculation?

I thank you for your answer.


Answer -
Hello,

I really don't want to go down that path, but if you insist,
here is what you could have written.
36 inches divided by 3/4 inches/book gives you 48 books.
Best to avoid mixing units with equal signs, it's a bad idea.

The only times that I've included units with any calculation are in chemistry and physics. Maths should be done with numbers in my humble opinion.

Answer
Numbers are fundamental to mathematical operations, while
units are not. By units, I don't mean "tens", "hundreds" and "thousands" in relation to the metric system; I mean physical attributes, such as measurements ("meters" versus "inches", "gram" versus "ounce" and so forth). Numbers need not be given any physical meaning in order for equations and the laws of mathematics to hold.

For instance, accountants in the UK and US calculate compound interest in the same way. The formula is still the same, the mathematical ideas are universal. It should not depend on the context or the environment.

One can easily interchange between pound sterlings and dollars after carrying out all the necessary calculations.

Units are there only to clarify things and remind us what we are dealing with in a particular situation. As long as we are consistent, we can do without units.

Hope this helps.