Big sale discounts are nice, but how much will that new video game, dress or even a new house really cost? In order to figure out how much of the cost the discount takes away and how much is left for you to pay, you'll have to master the concept of percentages.
TL;DR (Too Long; Didn't Read)
Sale price = original price × (1 − percent of discount). For this to work, the percent of discount must be expressed as a decimal.
Defining Percent of a Price
"Percent" actually means "out of one hundred," so it might help to think of the item's price as a pie that's been cut into one hundred tiny, equal parts. The percentage of the discount is how many of those itty-bitty pieces get taken away, and the number of pieces left indicates the percent of the original price that you pay. So if that dress you're looking at is on sale at a 30 percent discount, once you take those 30 percent pieces away you'll have 100 − 30 = 70 percent pieces left. So you'll end up paying 70 percent of the original price.
Calculating the Sale Price
Now that you understand how the percent discount relates to the sale price, it's time to find the sale price. Consider the example of a video game that costs $60, but is on sale for 10 percent off. How much will the sale price be after you take the discount?
Subtract the percent of the discount (in this case, 10 percent) from 100 to find how much of the original price you'll still pay. In this example, that means:
So the sale price of the video game will be 90 percent of the original price.
Divide by 100 to convert the result of the previous step to a decimal. So the percentage that represents your sale price becomes:
Multiply the decimal result from Step 2 by the original price of the game. Since the game originally cost $60 and you know you'll be paying 90 percent (or 0.9, in decimal form) of that price after taking the sale discount, you have:
The result of this step is your sale price after taking the discount.
Calculating Backward to the Original Price
Do you have the sale price of an item and want to know what the original price was? If you know the percent of the discount taken, you can figure it out. Consider a jacket that cost $90 on sale, after taking a 20 percent discount. What was the original price?
Subtract the percentage of the discount from 100. The result is the percentage of the original price that you paid. In this case, that means:
So the price you paid – in this case, $90 – represents 80 percent of the original cost.
Divide your result from the previous step – here, that's 80 percent – by 100 to convert it to a decimal:
Divide the sale price of the item – in this case, $90 – by the percentage paid of the original price. The result will be the original price of the item, before taking any sale discounts. Since you know you paid 80 percent or 0.8 of the original price, that works out to:
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About the Author
Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.