Math CentralQuandaries & Queries


Question from Kenneth:

Is it incorrect to have a proportion with numbers containing units that are not the same on both sides of the equal sign?

Here is an example: $0.07/$1.00 = ?/$0.89 is okay, but if I add a different unit (20 ounces) to one side of the equal sign but not the same unit to the other, is the proportion incorrect?

$0.07/$1.00 = ?/$0.89/20 ounces.

In order to determine the missing amount, the calculation becomes ($0.07/$1.00)/$0.89/20 ounces = $?, but is this proportion correct with the units as they are?
Two dollar-units cancel leaving dollar/ounces equals $?/ounces, but is this correct?

I thank you for your reply and answer.

Ratios and proportions with mixed units are fine provided the units balance.

Common special cases:

Same unit ratio on each side:

2litres/100km = 3 litres/150km

Each side individually balanced:

2litres/3litres = 100km/150km

In general, dimensional analysis justifies weirder combinations.
For instance, energy has the dimension mass*length2/time2 and
momentum has the dimension mass*length/time so you can equate
energy/momentum = length/time. This one is better left to trained professionals.

Good Hunting!

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