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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

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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