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					Learning about


  Using Inverse Operations for finding
  the original price after a percentage
          increase or decrease
To find a percentage of a number,
you..


         Divide the percent by 100


         And multiply by the number


            12% of 40 =
                                      Notice that  100
                                      changes the % to
 12  100
                                         a decimal
 (= 0.12) X 40
             = 4.8
If you wanted to
                                          The increased amount
increase 40 by 12%
                                            is (100 + 12)%
                                             of the original
         Find 12% of 40
         and then add this answer to 40




 112% of 40 = 4.8 + 40
                                     Notice that 112 100
 112  100 (= 1.12) X 40              changes the % to
                                         a decimal
             = 44.8                     which is 1.12
If you wanted to
decrease £125 by 23%                      The reduced amount
                                           is (100 - 23)%
Find 23% of 125                            of the original
and then subtract this answer from 125


   23  100 x 125 = 28.75
   £125 - £28.75 = £96.25
                                         Notice that 77 100
                                          changes the % to
                                             a decimal
  77  100 (= 0.77) X 125                   which is 0.77
            = £96.25
To increase by a percentage




  Input                       Output

     40         X 0.12         4.8


     40         X 1.12         44.8
Using inverse operations!

Insurance costs have increased by 12%     The cost after the increase is £44.80



   Input                                    Output
          ?                X 1.12           44.8
           What was the cost before the increase?

                                                                It cost
                                                                  £40
       40                     1.12           44.8
                                                              before the
                                                               increase
   Using inverse operations!

Insurance costs have increased by 23%        The cost after the increase is £88.56


      Input                                    Output
             ?                 X 1.23          88.56
              What was the cost before the increase?
                                                                      It cost
                                                                        £72
                                                                    before the
          72                     1.23           88.56               increase
To decrease by a percentage



  Input                                Output
  125           X 0.23
                                       28.75

          What is £125 minus £28.75?


   125           X 0.77                96.25
Using inverse operations!

In a sale stock is reduced by 23%             The sale price of a suit is £96.25


   Input                                     Output
                                                              The sale price is
          ?                  X 0.77        96.25              (100-23)% of the
                                                              original price


             What was the cost before the increase?


                                                                 It cost
                                                                  £125
       125                       0.77      96.25              before the
                                                                   sale
Using inverse operations!

In a sale stock is reduced by 18%                     The sale price of a suit is £96.25


   Input                                             Output
                             X 0.82
                                                                        The sale price is
          ?                                         96.25               (100-18)% of the
                                                                        original price


            What was the cost before the increase?

                                                                         It cost

                                 0.82
                                                                        £117.38
117 .38
                                                    96.25              before the
                                                                           sale

                          Round to 2dp for money!

				
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