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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