What Is 32 9 as a Mixed Number

Improper Fractions and Mixed Numbers

1. Definitions of Improper Fractions and Mixed Numbers

   In your pocket, you have five quarters.  Their are two ways of mentioning your cash.  The first way is five quarters or 5/4 dollars.  The second way is one dollar and a quarter or 1� dollars.  Both of these represent the same amount of money, however they are written in very different ways.  We define

   A proper fraction is a fraction smaller than one (the denominator is larger than the numerator)         2        5         7         3        5
   ,   ,   ,  , are all proper fractions
   9        10      32        4        7 An improper fraction is a fraction greater than or equal to one (the numerator is larger or the same as than the denominator        12       8        16       21       1
   ,   ,   ,  , are all improper fractions
   5        8        13        2        1 A mixed fraction is the sum of a whole number greater than zero and a proper fraction
   
             1            4             2             7           11
   6 ,    4     ,  1     ,  7  ,    2 are all mixed fractions
   4            7            13            8           12

2. Changing an Improper Fraction to a Mixed FractionWe have already learned how to do all of the work in changing an improper fraction to a mixed fraction when we learned how to perform long division with a remainder.  Now we just need to learn how to write down the answer.

   Example

   Convert

           22
   
   7into  a mixed number Solution We divide

                  3
   7 | 22

   21
   1The result is 3R1. Now to write this as a mixed number, the whole number part is 3 the numerator is 1 and the denominator is the original denominator 7
   

           22               1

       =  3
   7                7 Exercises
   
   Convert the following improper fractions to mixed numbers
   
   

   1.         53
      
      6
      Hold mouse over the yellow rectangle for the solution
      

   2.         92
      
      63
      Hold mouse over the yellow rectangle for the solution
      
      

   3.         9321
      
      32Hold mouse over the yellow rectangle for the solution
      

3. Changing a Mixed Fraction to an Improper Fraction Warm up problem Write the number 4 as an improper fraction with denominator 3.

   Solution

   We write

                    4 x 3               12
   4  =    =
   3                   3 To change a mixed fraction to an improper fraction we write the whole number as a fraction with the given denominator and then add the numerators.
   
   Example Write the mixed fraction         3�

   as an improper fraction

   Solution

   Write

   
   3           3 x 4           3
   3   =   +
   4              4              4

                   12 + 3           15
   =

      =
   4                4 Exercises
   
   Convert the following mixed fractions to improper fractions
   
   

   1.           5
      7
      6
      Hold mouse over the yellow rectangle for the solution
      
      

   2.            1
      2
      16
      Hold mouse over the yellow rectangle for the solution

   3.           12
      5
      13
      Hold mouse over the yellow rectangle for the solution

4. Reducing Improper Fractions and Mixed Numbers To reduce a mixed fraction, we need only reduce the fractional part of the mixed fraction by pulling out the common factor.

   Example

   Reduce

                9
   18
   30 Solution
   
   We have

            9                3 x 3                3

      =    =
   30            2 x 3 x 5            10 So

                9                    3
   18

       =   18
   30                  10 To reduce an improper fraction, we can cancel common factors just as we did with proper fractions.

   Example

   Reduce

   102
   
   68 Solution 102                2 x 51            2 x 3 x 17
       =    =
   68                2 x 34            2 x 2 x 17

                   3
   =

   
   2 For an improper fraction with a large numerator, it is easier to first convert the fraction to a mixed fraction then reduce.

   Example
   
   Reduce

   35682
   
   15 Solution
   
   Divide first
   
   2378
   15| 35682
   - 30
   56
   - 45
   118
   - 105
   132
   -  120
   12 Hence 35682                        12
       =    2378
   15                          15 Now reduce the fractional part 12             2 x 2 x 3          4
     =  =
   15                3 x 5             5 Putting the two results together gives 35682                        12                      4
       =    2378   =  2378
   15                          15                      5 Exercises Reduce the following.  Write your answer as a mixed fraction.

   1.           24
      4
      64
      Hold mouse over the yellow rectangle for the solution
      
      

   2.         42
      
      36
      Hold mouse over the yellow rectangle for the solution

   3.         26234
      
      18
      Hold mouse over the yellow rectangle for the solution
      

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What Is 32 9 as a Mixed Number

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