Math CentralQuandaries & Queries


Question from Kenneth:


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 $\$5 \times 7$ 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.

I thank you for your reply.

Yes. The units can be though of as "per-dollars" or $ \$^{-1}.$ Multiplying a number with such a dimension by a number with the dimension "dollars" yields a dimensionless number.

So for instance if we are told that $35$ unspecified items cost $\$5,$ we can perform the calculation you describe above to determine that the items are seven per dollar. To find out how many you get for $ \$3,$ multiply $(\$3)\times(7 \$^{-1} )$ to get a dimensionless $21$ as your answer.

Good Hunting!

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