Home > Pre-Algebra > Percentages > Percentage Sale Price

## Percentage Sale Price

#### Introduction

Percentage is a way of expressing a number as a fraction of 100. Percentages take a number and split it into 100. You can then express segments of the whole in terms of percentages. For example, if you find 20% of something, you would split the total number into 100 and then take 20 of those 100 segments.

Percentages are commonly used to express sales. You regularly see offers in stores or online giving '20% off' or you may receive a student discount of 10%. Working out how much these items cost after the discount is applied requires you to know how to calculate percentages.

## Lesson

The first step to take when an item is discounted is to calculate what percentage of the cost remains. For example, if a pair of shoes is discounted 20%, you need to know what percentage of the shoes' price you will need to pay.

To do this, subtract the percentage discount from 100. This will give you the remaining percentage. Let's use the following example:

A shirt in a store normally costs $80. However, there is a 15% off sale. What is the new cost of the shirt? (We will assume in this example that there is no tax to pay) So, the discount is 15%, so we should subtract 15 from 100 to find out what the remaining cost of the shirt is. $100 - 15 = 85$ Therefore, the cost of the shirt is 85% of the original total. Next, we need to work out what 85% of $80 is. There are two ways to do this. To do both, you will need to remember that 85% is the same as$ rac{85}{100}$.

The first way is to divide $80 by 100 to find 1% and then multiply that by 85. $\80 ÷ 100 = 0.8$ $0.8 x 85 = \68.00$ Therefore, the cost of the shirt after the discount is$68.00.

The second way to calculate the sale price of the shirt is to combine the two steps of the previous method. You can turn all percentages into decimals by just remembering that 100% is the same as 1.0. That means that if you place the number of the percentage after the decimal point, you will have converted it into a decimal.

For example, 85% is the same as 0.85. 75% is 0.75, 13% is 0.13 and so on.

To work out the cost of the shirt after the discount is applied, we can just multiply the original price by the decimal we have made:

$\80 x 0.85 = \68.00.$

This gives us the same answer. You can use either method. The second one is faster, so when you are more comfortable with decimals and percentages, you will usually find this one better.

## Examples

Ella saw a basketball on sale for \$5, with an additional 45% off. What was the final price of the basketball? The discount is: $0.45$ * KaTeX parse error:$ within math mode = KaTeX parse error: $within math mode Subtract the discount from the original price to find the sale price: KaTeX parse error: Unexpected character: '' at position 1: ̲.00 - .25 =$\$…