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QUESTION: Hello:

Can you explain why the following division is incorrect? The divisor has units, but the dividend does not.

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) are correct.

I thank you for your reply.

ANSWER: Hi Kenneth,

Well, there is nothing incorrect about 35/$5.00, you just have to be able to interpret what it represents. For instance, if you bought 35 oranges for $5.00 then the cost can be written as

35 oranges / $5.00 = 7 oranges/$ (read as seven oranges per dollar)

which just means that for one dollar you can buy 7 oranges. Even inverting the fraction does no harm, you can still write the cost as

$5.00 / 35 oranges = $1.00 / 7 oranges

again having the same meaning since 7 oranges equate to $1.00

In the case of a pure quantity, 35/$5.00 = 7/$

It is not uncommon to have units in denominator form. You can already see this when writing the unit of speed as meters/second.

I hope it helps.

Regards

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply.

I understand what you have indicated in your reply, but in order to make sense out of 35/$5.00, you added another unit to the 35, oranges. My original question is to indicate that 35/$5.00 does not make sense the 35 is a non-unit amount or number.

I thank you for your follow-up reply.

Hi Kenneth,

I understand what you're trying to point out here, that 35/$5.00 doesn't seem to have a particularly physical meaning. That could be true but there is nothing wrong with it algebraically.

To go further with the matter, let me ask you this; it is easily understood what it means to divide $35.00 into 5 places but what does it mean to divide $35.00 by $5.00? Of course the answer is 7 but what does it mean? Considering things physically, we can only understand dividing things into number of places. The algebraic statement; $35.00/$5.00 = 7 is a consequence of the more naturally understood statement $35.00/7 = $5.00

The point here is that a lot can be achieved through algebraic manipulations and it's possible that physical meanings might become unclear but usually it still makes sense if we follow the mathematical arguments.

So, to address your question, 35/$5.00 only seems abstract because 35 is abstract. I mean, no one has ever seen 35 :)

Regards

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Comment | Thanks for the reply and explanation to my follow-up question! |

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