Expert: Josh - 2/28/2005

Question
Hello:

I thank you for your reply. However my question was not exactly answered.

Is it possible for a mixed number like 1 1/2 to be inverted to 2/3 without first converting it to the improper fraction 3/2?
If so, can you demonstrate this procedure?

I thank you for your follow-up reply.

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Followup To
Question -
Hello:

Can a mixed number like 1 1/2 be inverted to 2/3 without first converting it to the improper fraction 3/2?

For example, the inverse of 1 1/2 or 3/2 is 2/3.

I thank you for your reply.
Answer -
I think most people would carry out the intermediate step in their head, rather than writing it down on paper.

Answer
I think the answer is a matter of perspective. To some people, flipping the fraction does not even count as a step. The truth is, no one knows how other people's brains work. For me, I go through the intermediate step. But, it is an implicit step. Getting the answer is like turning on the light switch. No one really gives much thought to it.

People who claim that this can be done in one step might not be telling a lie. There are many ways of doing a problem. Maybe they learned the basic arithmetic a little differently. Instead of finding the inverse of 1 1/2 = (2+1)/2 = 3/2, they can reverse the role of the numerator and denominator to start with. Instead of finding the common denominator (as you normally would), they concentrate on finding a common numerator in
1 2/1. The normal rules of mathematics are bent in the opposite sense.

Going from 1 2/1 to "2/2 + 2/1"
where addition is defined as 2/(2+1) = 2/3.

In the end, for something this simple, we gain nothing. It all comes down to how someone's brain works.