The __ how to work out percentages__ page showed how one can find a percentage of a certain amount or quantity.

Along with how to establish an original amount, if a new amount was the result of the original being increased or reduced by a certain percentage value.

It is also possible to find out the value of increase or decrease by percentage. When you know an original amount, and the new increased or decreased amount.

To find out how much an amount has increased by percentage wise, we can use the increase of percentage formula, shown below.

**100**

__Examples    __

*(1.1) *What is the increase in percentage from  16  to  20.

*Solution*   Increase Amount  = 

**20 − 16** = 

**4**

Original Amount  = 

**16**

Percentage Increase  =  \bf{\frac{4}{16}}  = 

**0.25**

(

**0.25**×

**100** = 

**25**)

The percentage increase from  16  to  20  is  50%.

*(1.2) *What is the percentage increase from  44  to  143.

*Solution*   Increase Amount  = 

**143 − 44** = 

**99**

Original Amount  = 

**44**

Percentage Increase  =  \bf{\frac{99}{44}}  = 

**2.25**

(

**2.25**×

**100** = 

**225**)

The percentage increase from  44  to  143  is  225%.

*(1.3) *What is the percentage increase from  2040  to  2142 .

*Solution*   Increase Amount  = 

**2142 − 2040** = 

**102**

Original Amount  = 

**2040**

Percentage Increase  =  \bf{\frac{102}{2040}}  = 

**0.05**

(

**0.05**×

**100** = 

**5**)

The percentage increase from  2040  to  2142  is  5% .

### Increase of Percentage Formula,

Further Examples

*(2.1) *A tin of soup in a grocery store was raised in price from  $1.32  to  $1.47 .

What was the percentage was the price of the tin of soup increased by?

*Solution*   Increase Amount  = 

**$1.56 − $1.30**=

**$0.26**

Original Amount  = 

**$1.30**

Percentage Increase  =  \bf{\frac{0.26}{1.30}}  = 

**0.2**

(

**0.2**×

**100** = 

**20**)

The tin of soup in the grocery store increased in price by  20%.

*(2.2) *What amount do you obtain when you increase 130 by a percentage of 40%?

*Solution*   {\frac{Increase \space Amount}{130}}  =  0.4

At this point we can now perform multiplication by  130  on both sides.

**130**× \bf{\frac{Increase \space Amount}{120}}  = 

**130**×

**0.4**

Increase Amount   =  

**52**

**130**+

**52** = 

**182**

So a percentage increase of  60%  from  130  is  182 .

## Decrease of Percentage Formula

As well as establishing the percent of increase when a smaller value increases to a larger value.

We can also work out the percent of decrease also, in cases where you have a larger amount that becomes a smaller amount.

Slightly different to the increase of percentage formula, there is a decrease of percentage formula.

So in a similar case to the increase of percentage formula, we just follow a few steps to obtain the percentage of decrease.

**1)**  Workout the decrease amount.

**2)**  Carry out division of this decrease amount by the original.

**3)**  Multiply the value of this division by 100.

__Examples    __

*(3.1) *What is the percentage decrease from  19  to  11.

*Solution*   **19**−

**11** = 

**8**

Decrease amount is  8.

( \bf{\frac{8}{19}} ×

**100**) %   =   (

**0.421**×

**100**) %   =  

**42.10**%

The percentage of decrease from  19  to  11  is around  42.10%,  due to  0.421  being rounded.

*(3.2) *What is the percent decrease from  1360  to  816.

*Solution*   **1360**−

**816** = 

**544**        Decrease amount is 544.

( \bf{\frac{544}{1360}} ×

**100**) %   =   (

**0.4**×

**100**) %   =  

**40**%

The percent decrease from  1360  to  816  is  75.86% .

*(3.3) *We can also use this method with decimal numbers.

What is the percent decrease from  2.6  to  1.196.

*Solution*   **2.6**−

**1.196** = 

**1.404**        Decrease amount is  1.404.

( \bf{\frac{1.404}{2.6}} ×

**100**) %   =   (

**0.54**×

**100**) %  = 

**54**%

The percent decrease from  2.6  to  1.196  is  54%.

*(3.4) *In a sale a video game was reduced in price from  $38  to  $27.55.

How much of a percentage decrease was the price reduction of the video game in the sale?

*Solution*   **38**−

**27.55** = 

**10.45**        Decrease amount is  10.45.

( \bf{\frac{10.45}{38}} ×

**100**) %   =   (

**0.275**×

**100**) %   =  

**27.5**%

The video game was reduced in price by  27.5%  in the sale.

*(3.5) *The amount of foxes in a forest decreased from  129  to  111  over two years.

*Solution*   **129**−

**111** = 

**18**        Decrease amount is  18.

( \bf{\frac{18}{129}} ×

**100**) %   =   (

**0.134**×

**100**) %  = 

**13.4**%

The amount of foxes in the forest decreased by around  13.4%  over the two year period.

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