   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: 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$\$5 \times 7$ 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.

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