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Division of Fractions

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    221445
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    Division of Fractions

     

    1. Dividing Two Proper or Improper Fractions

      To divide two proper or improper fractions we turn the problem into a multiplication problem by multiplying by the reciprocal

      Example

              3         2              3        5                15
                    ÷           =           x            =                                                
              4         5              4        2                 8



      Example

              2          4              12        515             5
                    ÷            =              x             =                                       
              9         15             
      39          24             6

      Exercises

      Divide
       
      1.         4          7          
                      ÷                                       
                5         11   


         
      2.         25         15          
                        ÷                                         
                16         56   


         
      3.          6           2          
                        ÷                                        
                 9           3   


         
    2. Division of a Whole Number By a Fraction

      In a division problem, when one of the numbers is a fraction and one a whole number, we can always write the whole number as a fraction with denominator 1.

      Example

      Divide


                      4              3         4                             3
             3  ÷           =           ÷           We write 3 =                                       
                      7              1         7                             
      1   

                        3         7                21
                =            x            =                                                
                        1         4                 4


      Example


              4                    4           2                                2
                    ÷  2   =           ÷               We write 2 =                                    
              5                    5           1                                
      1


                     24        1                 2
              =            x            =                                                      
                      5         
      12               5

      Exercise

      Divide
       
      1.         9                   
                      ÷  6                            
                7                   


         
      2.                   20          
               15  ÷                                         
                           3        


         
    3. Dividing Mixed Numbers

      Recall that when we multiplied mixed numbers we first needed to convert the mixed numbers into improper fractions.  Then we can multiply.  We use the same technique for division

      To divide mixed numbers, first convert to improper fractions then do the division

      Example

                1            2            5 x 2 + 1          3 x 3 + 2           11          11     Convert
            5        ÷  3         =                       ÷                      =            ÷                   to                            
                2            3                  2                       3                  2            3   
      improper fractions


                     111        3               3              1
              =            x            =              =  1                                         
                      2         
      111             2              2

      Exercises

      Divide
       
      1.           3            4      
              6        ÷  1                       
                  4            5     


         
      2.           2          8      
              2        ÷                         
                  7          9     



         
    4. Application

      Example

      You have 12 1/2 cups of flower left in the cupboard.  A batch of cookies requires 1 2/3 cups of flower.  How many batches of cookies can you make?

      Solution

      This is the division problem 

                  1            2          12 x 2 + 1              1 x 3 + 2             25          5
            12        ÷  1        =                         ÷                          =             ÷                                   
                  2            3                 2                            3                   2           3

                     
      525        3              15             1
              =            x            =              =  7                                         
                      2         
      15               2              2

      You can make 7 1/2 batches of cookies.

      Exercise

      You have decided to build a 100 yard boat dock and divide the dock up into slots for boats.  If each slot requires 3 1/4 yards of space how many slots can you construct?

       

     



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