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   
      Hold mouse over the yellow rectangle for the solution  44/35

    2.         25         15          
                                                               
              16         56   
      Hold mouse over the yellow rectangle for the solution  35/6
    3.          6           2          
                                                              
               9           3   
      Hold mouse over the yellow rectangle for the solution  1

  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                   
      Hold mouse over the yellow rectangle for the solution  3/14
    2.                   20          
             15                                           
                         3        
      Hold mouse over the yellow rectangle for the solution  9/4

  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     
      Hold mouse over the yellow rectangle for the solution  3 3/4

    2.           2          8      
            2                                 
                7          9     
      Hold mouse over the yellow rectangle for the solution  2 4/7


  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?

    Hold mouse over the yellow rectangle for the solution  You have space for 30 10/13 slots

 



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