# Increase of Percentage Formula,Decrease of Percentage Formula

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.

Percentage of Increase   =   \bf{\color{purple}\frac{Increase \space Amount}{Original \space Amount}} × 100

Examples &nbsp &nbsp

(1.1)&nbsp

What is the increase in percentage from &nbsp16&nbsp to &nbsp20.

Solution&nbsp &nbsp

Increase Amount &nbsp=&nbsp 20 − 16 &nbsp=&nbsp 4

Original Amount &nbsp=&nbsp 16

Percentage Increase &nbsp=&nbsp \bf{\frac{4}{16}} &nbsp=&nbsp 0.25

( 0.25 × 100 &nbsp=&nbsp 25 )

The percentage increase from &nbsp16&nbsp to &nbsp20&nbsp is &nbsp50%.

(1.2)&nbsp

What is the percentage increase from &nbsp44&nbsp to &nbsp143.

Solution&nbsp &nbsp

Increase Amount &nbsp=&nbsp 143 − 44 &nbsp=&nbsp 99

Original Amount &nbsp=&nbsp 44

Percentage Increase &nbsp=&nbsp \bf{\frac{99}{44}} &nbsp=&nbsp 2.25

( 2.25 × 100 &nbsp=&nbsp 225 )

The percentage increase from &nbsp44&nbsp to &nbsp143&nbsp is &nbsp225%.

(1.3)&nbsp

What is the percentage increase from &nbsp2040&nbsp to &nbsp2142&nbsp.

Solution&nbsp &nbsp

Increase Amount &nbsp=&nbsp 2142 − 2040 &nbsp=&nbsp 102

Original Amount &nbsp=&nbsp 2040

Percentage Increase &nbsp=&nbsp \bf{\frac{102}{2040}} &nbsp=&nbsp 0.05

( 0.05 × 100 &nbsp=&nbsp 5 )

The percentage increase from &nbsp2040&nbsp to &nbsp2142&nbsp is &nbsp5%&nbsp.

### Increase of Percentage Formula,Further Examples

(2.1)&nbsp

A tin of soup in a grocery store was raised in price from &nbsp$1.32&nbsp to &nbsp$1.47&nbsp.

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

Solution&nbsp &nbsp

Increase Amount &nbsp=&nbsp $1.56 −$1.30 = $0.26 Original Amount &nbsp=&nbsp$1.30

Percentage Increase &nbsp=&nbsp \bf{\frac{0.26}{1.30}} &nbsp=&nbsp 0.2

( 0.2 × 100 &nbsp=&nbsp 20 )

The tin of soup in the grocery store increased in price by &nbsp20%.

(2.2)&nbsp

What amount do you obtain when you increase 130 by a percentage of 40%?

Solution&nbsp &nbsp

{\frac{Increase \space Amount}{130}} &nbsp=&nbsp 0.4

At this point we can now perform multiplication by &nbsp130&nbsp on both sides.

130 × \bf{\frac{Increase \space Amount}{120}} &nbsp=&nbsp 130 × 0.4

Increase Amount &nbsp = &nbsp 52

130 + 52 &nbsp=&nbsp 182

So a percentage increase of &nbsp60%&nbsp from &nbsp130&nbsp is &nbsp182&nbsp.

## 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.

Percentage of Decrease &nbsp = &nbsp \bf{\color{purple}\frac{Decrease \space Amount}{Original \space Amount}} × 100

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

1)&nbsp Workout the decrease amount.

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

3)&nbsp Multiply the value of this division by 100.

Examples &nbsp &nbsp

(3.1)&nbsp

What is the percentage decrease from &nbsp19&nbsp to &nbsp11.

Solution&nbsp &nbsp

1911 &nbsp=&nbsp 8

Decrease amount is &nbsp8.

( \bf{\frac{8}{19}} × 100 ) % &nbsp = &nbsp ( 0.421 × 100 ) % &nbsp = &nbsp 42.10%

The percentage of decrease from &nbsp19&nbsp to &nbsp11&nbsp is around &nbsp42.10%,&nbsp due to &nbsp0.421&nbsp being rounded.

(3.2)&nbsp

What is the percent decrease from &nbsp1360&nbsp to &nbsp816.

Solution&nbsp &nbsp

1360816 &nbsp=&nbsp 544 &nbsp &nbsp &nbsp &nbsp Decrease amount is 544.

( \bf{\frac{544}{1360}} × 100 ) % &nbsp = &nbsp ( 0.4 × 100 ) % &nbsp = &nbsp 40 %

The percent decrease from &nbsp1360&nbsp to &nbsp816&nbsp is &nbsp75.86% .

(3.3)&nbsp

We can also use this method with decimal numbers.

What is the percent decrease from &nbsp2.6&nbsp to &nbsp1.196.

Solution&nbsp &nbsp

2.61.196 &nbsp=&nbsp 1.404 &nbsp &nbsp &nbsp &nbsp Decrease amount is &nbsp1.404.

( \bf{\frac{1.404}{2.6}} × 100 ) % &nbsp = &nbsp ( 0.54 × 100 ) % &nbsp=&nbsp 54 %

The percent decrease from &nbsp2.6&nbsp to &nbsp1.196&nbsp is &nbsp54%.

(3.4)&nbsp

In a sale a video game was reduced in price from &nbsp$38&nbsp to &nbsp$27.55.

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

Solution&nbsp &nbsp

3827.55 &nbsp=&nbsp 10.45 &nbsp &nbsp &nbsp &nbsp Decrease amount is &nbsp10.45.

( \bf{\frac{10.45}{38}} &times 100 ) % &nbsp = &nbsp ( 0.275 × 100 ) % &nbsp = &nbsp 27.5 %

The video game was reduced in price by &nbsp27.5%&nbsp in the sale.

(3.5)&nbsp

The amount of foxes in a forest decreased from &nbsp129&nbsp to &nbsp111&nbsp over two years.

By roughly what percentage had the amount of foxes in the forest decreased over the two years?

Solution&nbsp &nbsp

129111 &nbsp=&nbsp 18 &nbsp &nbsp &nbsp &nbsp Decrease amount is &nbsp18.

( \bf{\frac{18}{129}} × 100 ) % &nbsp = &nbsp ( 0.134 × 100 ) % &nbsp=&nbsp 13.4 %

The amount of foxes in the forest decreased by around &nbsp13.4%&nbsp over the two year period.

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