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# Basic Math/Division With & Without Units

Question
Hello:

Would there be a reason to divide a number without units by another number with units?  Here is an example:

35 divided by \$5.00 or 35/\$5.00

The answer cannot have units (\$) because \$5 X 7 does not equal 35 but instead \$35.00.

\$35.00 divided by 5 or (\$35.00/5) and \$35 divided by \$5.00 or  (\$35.00/\$5.00) make more sense.

Yes, but I say that in practice we can attach units to just about anything.

Some examples:
1. \$35 divided by 5, we can think of \$35 being split 5 ways, say among 5 people
.  Thus, \$35/5 ppl = \$7 per person.

2. 35 divided by \$5, we can think of \$5 buys us 35 of something, say 35 eggs.
.  Thus, 35 eggs/\$5 = 7 eggs/\$ or 7 eggs per dollar, i.e. \$1 dollar buys us 7 eggs.

See?

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Basic Math

Volunteer

#### Abe Mantell

##### Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

##### Experience

Over 15 years teaching at the college level.

Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook