Expert: Josh - 1/31/2008

Question
Hello:

I have a question regarding division with units.


1)  6 gallons/3 = 2 gallons.
Is this type of division with one unit correct.

(2)  6 gallons/2 gallons = 3
Is this type of division with the same units correct.

(3)  6 miles)/2 gallons = 3 miles/1 gallon
Is this type of division with different units correct.

(4)  However, 6/2 gallons = ?
Is this example correct or incorrect? It seems incorrect to me.

I thank you for your reply.

Answer
Dear Kenneth

I am reluctant to say if any of them are "correct". As I mentioned last time, mathematical syntax is perfectly understandable without the need of further annotation such as scientific units. Only the person who wrote the equation knows what situation it actually describes. I can say, however, that we can rationalize (1) and (2) as follows, but what the person actually had in mind is anyone's guess.

For (1), it is consistent with the question, "given 6 gallons of a liquid, if we divide it equally between three barrels, how much would each barrel contain?" The answer will be given in units of "gallon"

For (2), perhaps we can match it to the following description. A round trip journey uses 2 gallon of fuel. Given 6 gallon, how many round trips can we take?

Again, I won't elaborate further on (3) and (4). It is pointless guessing what situation the equations may describe. But it looks as if (3) is just a fuel economy (rate) calculation.

Regards,
J