Have you ever found yourself in the store, trying to figure out what the actual price is on something that's on sale for a set percentage off – say, 25 percent or 30 percent? "Percent" means out of 100, so when you take a percentage off, it's as if someone has cut whatever you're measuring into 100 equal pieces. Then you remove however many of those equal pieces the percentage tells you to remove. Fortunately, once you know how to calculate percentages, you can figure out percentage discounts with just a couple of simple operations – no actual cutting or removing needed.
Calculating Percent Off
In order to calculate how much you're saving on a sale item, you need to know the original price of the item and the percent of the discount being applied.
Convert the Percentage to a Decimal
Divide the percentage discount by 100 to convert it to a decimal. So if that dress is on sale for 25 percent off, you have:
25 ÷ 100 = 0.25
Multiply the Original Price by the Discount
Multiply the original price of the item by the percent discount. The result will be the amount of the discount in dollars, or the amount of money you save in the sale. If the dress originally cost $80, you have:
$80 × 0.25 = $20
So if the dress originally cost $80 and it's on sale for 25 percent off, you stand to save $20. It should be intuitively clear that this means you'll pay $60, but if you're calculating percentages for a math problem, you might need to explicitly show that [original price] - [discount in dollars] = [sale price]. Or:
$80 - $20 = $60 is the new price of the dress on sale.
Going Straight to the Sale Price
Sometimes you have to pay close attention to math problems (and real-world problems) to figure out what information you need. If what you really need to know is an item's final sale price after the discount is taken, you can skip calculating the discount's dollar amount and go straight to figuring what's left after you remove the discount. Imagine that you've seen a blazer in the shop window that originally sold for $90, but now it's on sale for 30 percent off.
Calculate the Percent Remaining After Discount
Subtract the percentage of the discount from 100; the amount left over will represent what remains of the original price after you've taken away the discount. To continue the blazer example, you have:
100 - 30 = 70 percent. Once you take the 30 percent discount, you'll be paying 70 percent of the original price.
Convert the Sale Price Percentage to a Decimal
Divide the percentage that represents the new sale price – in this case, 70 percent – by 100 to convert it to a decimal:
70 ÷ 100 = 0.7
Multiply the Price Percentage by the Original Price
Multiply the original price and the percentage that represents the sale price; the result is the sale price of the blazer in dollars:
$90 × 0.7 = $63. So if the blazer is on sale for 30 percent off, you'll pay the remaining 70 percent of the price, which is $63.