Expert: Bobby Soltani - 5/17/2005

Question
Hello:

I want to thank you for the reply.

When converting pounds to ounces and ounces to pounds, do these processes involve determining how many ounces are in pounds, as in how many 64 ounces are in 4 pounds, and how many pounds are in ounces as in how many 4 pounds are in 64 ounces, both of these involve division because of the question, how many ... are in ...?

I thank you for your follow-up reply.
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Followup To
Question -
Hello:

Does the process of unit conversions involve using division or multiplication or both?

It requires a unit factor, used to multiply not divide, in most cases although the 1 pound is used as a divisor, but 4 pounds in multiplied by 16 ounces/1 lb.

Example:
4 lbs X (16 ounces/1 lb) = 64 ounces

If the process is reversed, converting 64 ounces to pounds, the process involves 64 ounces X (1 lb/16 ounces) = 4 lbs.

Here it appears that division is used: 64 ounces divided by 16 ounces then multiplied by 1 pound.

So is multiplication or division the main mathematical operation used in converting units?

I thank you for your reply.
Answer -
Hi,

Actually, either can be used.  Multiplication and division can be used interchangeably.  For instance:

4 lbs X (16 ounces/1 lb) = 64 ounces

or

4 lbs / (1 lb / 16 ounces) = 64 ounces

So, we get the same result using either.  That is because multiplying by 16 is the same as dividing by (1/16), and vise versa.

Let me know if you have any questions.

Bobby


Answer
Hi,

I think what you are saying is correct.  The purpose of finding how many ... in .... is so that we can muliply or divide things by 1 and not change anything.  Anytime you multiply something by 1, it equals the same number. Example:

5 *(200/200) = 5

So if 16 oz = 1 lb, we can divide both sides of the equation by 1 lb and get:

(16 oz)/(1 lb) = 1

So now, we can multiply anything by (16 oz)/(1 lb) and the value does not change.  Example

3 lb * (16 oz)/(1 lb) = 48 oz

Note, the lb cancels because we have one in the numerator and one in the denominator.  We are left with the equivalent of 3 lb expressed in ounces.

I hope this helps.  Let me know if you still have any questions.

Bobby