Math Percentage calculation Percentage change

# Percentage change

If a size increases/ decreases by a percentage value, you have to add it to/ subtract it from the initial size.

initial size $\pm$ percentage change = final size

### Examples

The inventory of a shop (2000 items) increased by 9 percent. Calculate the new stock.

$2000+9\%\cdot2000$ $=2000+180$ $=2180$

There is a 5% discount on a mobile phone that costs 300€. Calculate the new price.

$300€-5\%\cdot300€$ $=300€-15€$ $=285€$

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### Remember

With a percentage change the initial inventory (100%) will increase/ decrease by r%.

Alternatively, you can set the value to $(100\%\pm r\%)$ or rather to $(1\pm\frac{r}{100})$.

## Percentage increase

With a percentage increase, you have to multiply the initial value $W$ with the increasing factor $(1+\frac{r}{100})$.

$W_{new}=W\cdot(1+\frac{p}{100})$

### Example

The inventory of a shop (2000 items) increased by 9 percent. Calculate the new stock.

$2000\cdot(1+\frac9{100})$ $=2000\cdot\frac{109}{100}$ $=2180$

## Percentage decrease

With a percentage decrease, you have to multiply the initial value $W$ with the decreasing factor $(1-\frac{r}{100})$.

$W_{new}=W\cdot(1-\frac{r}{100})$

### Example

There is a 5% discount on a mobile phone that costs 300€. Calculate the new price.

$300€\cdot(1-\frac5{100})$ $=300€\cdot\frac{95}{100}$ $=285€$

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### Hint

If the final size and the factor are known and the initial size is wanted, you have to change the formula beforehand:

$W_{new}=W\cdot(1\pm\frac{r}{100})\quad|:(1\pm\frac{r}{100})$
$W=W_{new}:(1\pm\frac{r}{100})$