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What is the name of a fraction like this:

$$\frac{22}{7}$$

as opposed to one like this:

$$3\frac{1}{7}$$

I've never actually had to describe this until today. Not only have I no idea how to describe the top-heavy fraction or the one with a whole number, I also don't even know what the process of changing from the former to the latter is called. Is it merely "simplifying"...? I have a feeling there must be a more technical name, because it's math and there always is.

Caveat: This is a very simple question, so much so that I feel sure it must be a duplicate. I did try to search but I was unable to come up with a succinct expression to describe what I am looking for (as evidenced by the fairly lame title of this question) and so the search came up empty.

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1 Answer

up vote 2 down vote accepted

The former is generally called an "improper fraction," the latter a "mixed number."

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Wow. That's nothing like what I was imagining. Google confirms you are correct, sir. Man, searching is so easy when you actually have the words to search for! –  David John Welsh Apr 4 '13 at 17:04
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Apparently I have to wait 11 minutes before I can accept. Eleven. Presumably Math.SE's time limits are all prime numbers or something.... –  David John Welsh Apr 4 '13 at 17:07
    
Frankly, I think I prefer "top-heavy fraction" as a term! –  Cameron Buie Apr 4 '13 at 17:33
    
@Cameron Me too, but even top-empty fractions prove handy at times. –  Math Gems Apr 4 '13 at 20:23
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So now we have busty fractions and topless fractions ... –  Brian M. Scott Apr 4 '13 at 21:44
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