Improper FractionsDate: 05/20/2002 at 05:42:56 From: Dana Subject: Fractions Dear doctors, My math teacher says that we read 14/9 as "fourteen ninths", but I think we should read it as "fourteen over nine" because the 14 can't be a part of nine parts. And do we have a fraction called "six halves"? If yes, how do we write it? Please help. I am really confused. Best regards. Date: 05/20/2002 at 12:11:01 From: Doctor Peterson Subject: Re: fractions Hi, Dana. In everyday speech, we think of a fraction as something less than one. If I said "a fraction of my coworkers were laid off today", I would mean a small part; if I said "a fraction of a percent of students understand the meaning of this word", I would mean less than one percent. But the root meaning of the word "fraction" is just "broken"; mathematically, a fraction can be made up of any number of pieces, even if, together, they make up more than a whole. Just imagine taking a bunch of pizzas and cutting each of them into eight parts. Now I might eat three of them myself, so I've eaten three eighths: 3/8 of a pizza. But someone else might take 21 pieces for his family of seven; he's taken 21 eighths, which is the fraction 21/8. Do you see that it really makes just as much sense to read this fraction as "twenty-one eighths", even though it is not part of just one pizza? Similarly, if I cut three apples in half, I would have six halves, which we can write as 6/2. Certainly there is a good reason for preferring, in many situations, to rewrite such an improper fraction as a mixed number, so that the fractional part is less than one as we expect; we call these fractions "improper" just because they do feel "wrong" to us. But since improper fractions still make sense, and are very useful in many situations, it is correct to read them the same way we read proper fractions. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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