Division of Fractions   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         4          7                         ÷                                                5         11    Hold mouse over the yellow rectangle for the solution          25         15                           ÷                                                  16         56    Hold mouse over the yellow rectangle for the solution           6           2                           ÷                                                  9           3    Hold mouse over the yellow rectangle for the solution  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         9                                  ÷  6                                     7                    Hold mouse over the yellow rectangle for the solution                    20                  15  ÷                                                             3         Hold mouse over the yellow rectangle for the solution  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           3            4             6        ÷  1                                  4            5      Hold mouse over the yellow rectangle for the solution            2          8             2        ÷                                    7          9      Hold mouse over the yellow rectangle for the solution  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    Back to the Fractions page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions