What's the difference between a discount and the sale price?

A discount is the amount of money you save (for example, saving $20 on a $100 item), while the sale price is what you actually pay (for example, $80). The discount is part of the original price, and when you subtract it, you get the sale price. The formula calculates the sale price directly.

Why do we subtract the discount percentage from 100 instead of just using it directly?

Because d is given as a percentage—a number out of 100. We divide by 100 to convert it to a decimal we can multiply with, so \frac{d}{100} becomes the fraction of price we remove. The expression (1 - \frac{d}{100}) is the fraction of the original price you actually pay.

Can the discount percentage be more than 100%?

In real life, no—a discount larger than 100% would result in a negative price, which is impossible. In practice, discounts range from 0% (no discount) to 100% (the item is free). If you ever calculate a negative sale price, you have made an error.

How is Discount and Sale Price different from Sales Tax and Tip?

With Discount and Sale Price, you subtract a percentage to reduce the cost: S = L\left(1 - \frac{d}{100}\right). With Sales Tax and Tip, you add a percentage to increase the cost: F = P\left(1 + \frac{r}{100}\right). Both formulas have the same structure but move in opposite directions—one reduces the amount, the other increases it.

Discount and Sale Price

Calculate the sale price after subtracting a discount percentage from the original list price of the item you're buying.

S = L\left(1 - \frac{d}{100}\right)

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What each symbol means

What Discount and Sale Price takes

Symbol	Meaning
$S$	The sale price, denoted $S$ , is the final amount you pay after the discount is applied, measured in dollars; if confused with the discount amount itself, you'll calculate what you save instead of what you pay.
$L$	The list price, denoted $L$ , is the original or regular price before any discount is applied, measured in dollars; if confused with the sale price, you'll substitute the wrong value into the formula.
$d$	The discount percentage, denoted $d$ , is entered as a whole number like 25 for 25% off, not a decimal like 0.25; if entered as a decimal, your final answer will be 100 times too small.

When to use it

Use this formula when you know an item's original price and need to find what you actually pay after a discount is applied.

Level

Usually taught in: Pre-Algebra

Worked examples

1. Simple percentage discount on shoes

Problem

A pair of shoes originally costs $80. They are on sale with a 20% discount. What is the sale price?

$S = 80\left(1 - \frac{20}{100}\right)$
We substitute the list price of 80 and discount percentage of 20 into the formula.
$S = 80\left(1 - 0.2\right)$
We convert the discount percentage to a decimal by dividing by 100: $20 \div 100 = 0.2$ .
$S = 80\left(0.8\right)$
We calculate $1 - 0.2 = 0.8$ to find what fraction of the original price we pay.
$S = 64$
We multiply to find the final sale price: $80 \times 0.8 = 64$ dollars.

Answer: $S = 64$

We substitute the known values into the formula and simplify by converting the percentage to a decimal, then using multiplication to find the final price. This straightforward problem tests whether you understand how a discount reduces the price by a given percentage.

2. Discount on a decimal price

Problem

A jacket originally priced at $65.99 has a 30% discount. What is the sale price?

$S = 65.99\left(1 - \frac{30}{100}\right)$
We substitute the list price of 65.99 and discount percentage of 30 into the formula.
$S = 65.99\left(1 - 0.3\right)$
We convert 30% to a decimal by dividing by 100: $30 \div 100 = 0.3$ .
$S = 65.99\left(0.7\right)$
We calculate $1 - 0.3 = 0.7$ to find what fraction of the original price remains after the discount.
$S = 46.193$
We multiply the list price by the fraction: $65.99 \times 0.7 = 46.193$ .
$S \approx 46.19$
We round to the nearest cent since we are working with currency: $46.193$ becomes $46.19$ dollars.

Answer: $S = 46.19$

This problem is more challenging because the original price includes cents, making the arithmetic more complex and requiring rounding at the end since currency is always expressed in cents. It tests your ability to handle realistic prices and decimal arithmetic.

3. Basketball jerseys on sale

Problem

During a back-to-school promotion, a sporting goods store is selling basketball jerseys with a 15% discount. If the regular price of a jersey is $45, what will you pay after the discount?

$S = 45\left(1 - \frac{15}{100}\right)$
We substitute the regular price of 45 and discount percentage of 15 into the formula.
$S = 45\left(1 - 0.15\right)$
We convert 15% to a decimal by dividing by 100: $15 \div 100 = 0.15$ .
$S = 45\left(0.85\right)$
We calculate $1 - 0.15 = 0.85$ , which tells us we pay 85 cents of every dollar of the original price.
$S = 38.25$
We multiply to find the final sale price: $45 \times 0.85 = 38.25$ dollars.

Answer: $S = 38.25$

Word problems require you to identify which number is the list price and which is the discount percentage from the problem text, then apply the formula exactly as you would with explicit numerical values. This shows how the discount formula applies to real-world shopping scenarios you encounter every day.

Common mistakes

Where Discount and Sale Price usually goes wrong

The mistake	Why it is wrong	The fix
Students write $S = 80 \times 0.2 = 16$ , calculating only the discount amount instead of the sale price.	They calculated what you save, not what you pay; the formula requires subtracting the discount from 1 first.	Use the complete formula $S = L\left(1 - \frac{d}{100}\right)$ where $(1 - \frac{d}{100})$ is the fraction of the price you actually pay. For $80 with 20% off: $S = 80(1 - 0.2) = 80(0.8) = 64$ .
Students write $S = 80(1 - 20) = 80(-19) = -1520$ , forgetting to divide the discount percentage by 100.	The discount must be converted to a decimal by dividing by 100; using the raw percentage number produces a meaningless negative result.	Always divide the discount percentage by 100 in the formula: $S = L\left(1 - \frac{d}{100}\right)$ . If the discount is 20%, write it as $\frac{20}{100}$ or $0.2$ , never as just 20.
Students calculate $S = 80 - 25 = 55$ when seeing a 25% discount, subtracting the percentage number as if it were a dollar amount.	They literally subtracted 25 from 80 instead of calculating 25% of 80 and subtracting that from the original price.	Use the formula to find the sale price: first convert 25% to a decimal by dividing by 100, then multiply by the list price. For $80 with 25% off: $S = 80\left(1 - \frac{25}{100}\right) = 80(0.75) = 60$ dollars.

Tips and when to use something else

The expression $(1 - \frac{d}{100})$ represents the fraction of the original price you pay—not the amount you save. For a 30% discount, you pay 70% of the original price.
This formula is related to Percent of a Number, since finding the sale price is equivalent to calculating what portion of the list price remains after subtracting the discount.
If you need to find just the discount amount (how much money you save), use Discount Amount $= L \times \frac{d}{100}$ , which gives you the dollar savings before subtracting from $L$ .
Always double-check that your sale price is less than the original price—if it is not, you have made an error in your calculation.

Related formulas

Percent of a NumberPercent of a Number finds how much you get when taking a percentage of a quantity—essential for tips, discounts, grades, and everyday calculations.Sales Tax and TipCalculate the total final amount you pay when adding a percentage—such as sales tax or tip—to the original price of any item.Order of OperationsOrder of Operations is the set of rules that tells you which calculation to do first when you have multiple operations in one expression.

Frequently asked questions

What's the difference between a discount and the sale price?: A discount is the amount of money you save (for example, saving $20 on a $100 item), while the sale price is what you actually pay (for example, $80). The discount is part of the original price, and when you subtract it, you get the sale price. The formula calculates the sale price directly.
Why do we subtract the discount percentage from 100 instead of just using it directly?: Because $d$ is given as a percentage—a number out of 100. We divide by 100 to convert it to a decimal we can multiply with, so $\frac{d}{100}$ becomes the fraction of price we remove. The expression $(1 - \frac{d}{100})$ is the fraction of the original price you actually pay.
Can the discount percentage be more than 100%?: In real life, no—a discount larger than 100% would result in a negative price, which is impossible. In practice, discounts range from 0% (no discount) to 100% (the item is free). If you ever calculate a negative sale price, you have made an error.
How is Discount and Sale Price different from Sales Tax and Tip?: With Discount and Sale Price, you subtract a percentage to reduce the cost: $S = L\left(1 - \frac{d}{100}\right)$ . With Sales Tax and Tip, you add a percentage to increase the cost: $F = P\left(1 + \frac{r}{100}\right)$ . Both formulas have the same structure but move in opposite directions—one reduces the amount, the other increases it.

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Reviewed 2026-09-18