Improper Fractions and Mixed Numbers

Date: 09/10/97 at 00:08:41
From: Ted Kim
Subject: Fractions

What do you do when the numerator of a fraction is bigger than 
the denominator?  Such as when the answer comes out as 4 and 7/6?

Date: 10/06/97 at 11:14:59
From: Doctor Sonya
Subject: Re: Fractions

What I would do is convert the 7/6, which is an "improper fraction,"
into a "mixed number" or "mixed fraction" or "mixed numeral," 
whichever you like to call it. (A mixed number is a number that has 
both a whole number and a fraction in it, like 2 1/2.)

The method for doing that is to:

  Divide the 6 into the 7, which goes 1 time and leaves a remainder 
  of 1.  

     7/6 = 1 remainder 1. 

  This gives you the whole number 1, with 1/6 left over.  

Another way to think  about what I did here is to write 

     7/6 = 6/6 + 1/6.

  You know that 6/6 = 1, so 7/6 = 1 + 1/6.

Back to your problem, 4 and 7/6 becomes 

     4 and 1 and 1/6, or 
     5 and 1/6, 

  which you can also write in e-mail as 5 1/6. 
  (Not 51/6) But "5 and 1/6" is clearer.

You may wonder why this works. Let's look at a number line going 
from 0 to 2, divided into 6ths.


0   1/6  2/6  3/6  4/6  5/6  6/6  7/6  8/6  9/6 10/6 11/6 12/6  
+----+----+----+----+----+----+----+----+----+----+----+----+
0                             1                             2
+----+----+----+----+----+----+----+----+----+----+----+----+
0                             1  1 1/6     1 3/6    1 5/6
                                      1 2/6    1 4/6      1 6/6

Note that I gave 8/6 two different names: 8/6 and also 1 and 2/6. 
If you know how to reduce fractions, you'll see that I could reduce 
1 and 2/6 to 1 and 1/3, or reduce 8/6 to 4/3, in either case by 
dividing both the numerator and the denominator by 2. If you don't 
understand that last sentence, don't worry about it.  I'm sure you'll 
cover how to reduce fractions soon.

Here are some more examples.

Suppose you have the fraction 39/8. Using the method I showed, 
divide 8 into 39, which goes 4 times, with a remainder of 7.  
Thus, 39/8 = 4 and 7/8.

If you had 2 and 13/5 to simplify, then do 5 into 13: it goes 2 times, 
with a remainder of 3. So 2 and 13/5 = 2 and 2 and 3/5 which means 
4 and 3/5.
 
I hope this helps.

-Doctors Guy and Sonya,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/