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Day 4: The reverse of a percentage increase or decreaseDescription: Undoing a percentage increase or decrease by the UNDO method.
Objective: The purpose of this module is to increase or decrease by a percentage by direct multiplication. When you increase a value by 30%, you are finding (100+30)%=130% of the value. Which you find by multiplying by 1.30 To UNDO that increase (which is NOT the same as decreasing by 30%) you do the opposite of multiplying by 1.30 which is dividing by 1.30 Similarly a 20% decrease is finding (100-20)% = 80% which is done by multiplying by 0.80 and UNDONE by dividing by 0.80
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When you increase a value by 30%, you are finding (100+30)%=130% of the value.

Which you find by multiplying by 1.30

To UNDO that increase (which is NOT the same as decreasing by 30%) you do the opposite of multiplying by 1.30 which is dividing by 1.30

 

When you decrease a value by 20%, you are finding (100-20)% = 80% of the value.

Which you find by multiplying by 0.80

To UNDO that decrease(which is NOT the same as increasing by 20%) you do the opposite of multiplying by 0.80

Which is dividing by 0.80

 

 

The Price of a car is decreased by 20%.  It now costs €1600.  How much did it cost before the decrease.

Method.  We want the Original Price of the car.  Or 100% of the Original Price of the car (Same thing)

 100% of the Original Price of the car - 20% of the Original Price of the car 

= 80% of the Original Price of the car 

We are told that this is 1600 euro.

i.e.  80% of the Original Price of the car  = 1600 euro

To DO this we would multiply the original price by 0.80

To UNDO this we would do the opposite of multiplying by 0.80

i.e.  Divide the 1600 by 0.80

= 2000 euro

To find  100% of the Original Price of the car we can also use the unitary method.

80% of the Original Price of the car  = 1600 euro

(Divide by 80)

1% of the Original Price of the car  = 1600 /80

(Multiply by 100)

100% of the Original Price of the car  = (1600 /80) x 100

The Original Price of the car  = (1600 /80) x 100

= 2000 euro.

 

 

Example Question Two

The Price of a car is increased by 25%.  It now costs €2000.  How much did it cost before the decrease.

Method.  We want the Original Price of the car.  Or 100% of the Original Price of the car (Same thing)

 100% of the Original Price of the car + 25% of the Original Price of the car 

= 125% of the Original Price of the car 

We are told that this is 2000 euro.

i.e.  125% of the Original Price of the car  = 2000 euro

To find  100% of the Original Price of the car we use the unitary method.

125% of the Original Price of the car  = 2000 euro

(Divide by 125)

1% of the Original Price of the car  = 2000 /125

(Multiply by 100)

100% of the Original Price of the car  = (2000 /125) x 100

The Original Price of the car  = (2000 /125) x 100

= 1,600 euro