Home > Pre-Algebra > Percentages > Percentage Decrease

## Percentage Decrease

#### Introduction

A percentage is an extremely useful system for comparing different number values. For example, if one shirt in a store is reduced from $100 to$80, you save $80. If a different shirt in the store is reduced from$50 to $35, that's a saving of$15. However, we can use percentages to work out which discount is bigger. This helps us to know which is the better deal.

## Lesson

To calculate the percentage decrease we need to follow the same steps every time:

1) Work out the amount of the decrease by subtracting the new value from the old one.

2) Divide the different by the old value, and multiply by 100 to turn it into a percentage.

Let's put it into practice.

Using the example in the introduction, the first shirt was discounted from $100 to$80. To work out the amount of the decrease, we would subtract 80 from 100.

$100 - 80 = ?$

$100 - 80 = 20$

Therefore, the decrease in cost was \$20.

We then take that decrease (20) and divide it by the original cost of the shirt (100).

$20 ÷ 100 = 0.2$

To turn this from a decimal into a percentage, we need to multiply it by 100.

$0.2 * 100 = 20%$

The first shirt was therefore discounted 20%

Let's repeat that with the second shirt, which was originally $50, but was reduced to$35.

Firstly, we subtract 35 from 50.

$50 - 35 = ?$

$50 - 35 = 15$

We then divide the decrease (15) by the original cost of the shirt (50).

$15 ÷ 50 = 0.3$

Then we multiply by 100 to find a percentage:

$0.3 x 100 = 30%$

Therefore, the second shirt was discounted 30%. That means the second shirt had a bigger discount than the first shirt.

## Examples

Joseph's construction project required he to cut a board from 14 feet to 13 feet. By what percent did the length of the board decrease?
First, find the number of feet cut
$14 - 13 = 1$
To find what percentage 1 is of 14, we need to divide
$\dfrac{1}{14} = 0.071$
Moving the decimal place two to the right and then putting a % sign at the end of the number we get:
$0.071$ = KaTeX parse error: Expected 'EOF', got '%' at position 4: 7.1%̲