How to Calculate a Discount

Calculating the Discount and Sale Price

Convert the percentage discount to a decimal. To do this, think of the percent number with a decimal to the right of the last digit. Move the decimal point two places to the left to get the converted decimal. You can also use the % {\displaystyle \%} \% sign on a calculator. For example, you might want to calculate the sale price of a pair of shoes that is regularly $69.95. If the shoes are 25% off, you need to convert 25% to a decimal by thinking 25 % = 25.00 % = .25 {\displaystyle 25\%=25.00\%=.25} 25\%=25.00\%=.25.

Multiply the original price by the decimal. You can multiply the decimal by hand, or use a calculator. This will tell you the discount, or what value is being taken off the original price. For example, to find the 25% discount on a pair of $69.95 shoes, you would calculate 69.95 × .25 = 17.49 {\displaystyle 69.95\times .25=17.49} 69.95\times .25=17.49.

Subtract the discount from the original price. To subtract decimals, line up the decimal points and subtract as you would whole numbers. Be careful to drop the decimal point down into your answer. You can also use a calculator. The difference will be the sale price of the item. For example, if a pair of shoes that are originally $69.95 have a discount of $17.49, calculate the sale price by subtracting: 69.95 − 17.49 = 52.46 {\displaystyle 69.95-17.49=52.46} 69.95-17.49=52.46. So, the shoes are on sale for $52.46.

Estimating the Discount and Sale Price

Round the original price to the nearest ten. Use normal rounding rules to round up or down. Doing this will make it easier to calculate the percent discount of the number. For example, if the original price of a shirt is $47.89, round the price up to $50.00

Calculate 10 percent of the rounded price. To mentally calculate 10% of a price, think of the price written as dollars and cents with a decimal point. Then, move the decimal point one place to the left. This will show you the number that is equal to 10%. For example, to calculate 10% of $50, think $ 50 = $ 50.00 = $ 5.00 {\displaystyle \$50=\$50.00=\$5.00} \$50=\$50.00=\$5.00. So, 5 is 10% of 50.

Determine the number of tens in the percent off. To figure out the number of tens, divide by the percentage by 10 using normal division rules. Don’t worry about fives in the percentage for now. For example, if a shirt is 35% off, you would need to know how many tens are in 35. Since 35 ÷ 10 = 3.5 {\displaystyle 35\div 10=3.5} 35\div 10=3.5, there are 3 tens in 35.

Multiply 10% of the rounded price by the appropriate factor. The factor is determined by the number of tens in the percent off. Since you determined what 10% of the price is, find a larger percent by multiplying by the number of tens. For example, if you found that 10% of $50 is 5, to find out how much 30% of 50 is, you would multiply $5 by 3, since there are 3 tens in 30: 5 × 3 = 15 {\displaystyle 5\times 3=15} 5\times 3=15. So, 30% of $50 is $15.

Calculate 5% of the rounded price, if necessary. You will need to do this step if the percent off discount ends in a 5 rather than a 0 (for example, 35% or 55% off). It is easy to calculate 5% by simply dividing 10% of the original price by 2, since 5% is half of 10%. For example, if 10% of $50 is $5, then 5% of $50 is $2.50, since $2.50 is half of $5.

Add the remaining 5% to the discount, if necessary. This will give you the total estimated discount of the item. For example, if a shirt is 35% off, you first found 30% of the original price was $15. Then you found that 5% of the original price was $2.50. So adding the values of 30% and 5%, you get $ 15 + $ 2.50 = $ 17.50 {\displaystyle \$15+\$2.50=\$17.50} \$15+\$2.50=\$17.50. So, the estimated discount of the shirt is $17.50.

Subtract the discount from the rounded price. This will give you an estimate of the sale price of the item. For example, if the rounded price of a shirt is $50, and you found the 35% discount to be $17.50, you would calculate $ 50 − $ 17.50 = $ 32.50 {\displaystyle \$50-\$17.50=\$32.50} \$50-\$17.50=\$32.50. So, a $47.89 shirt that is 35% off is about $32.50 on sale.

Completing Sample Problems

Calculate the exact sale price. A television is originally priced at $154.88. It now has a 40% discount. Convert the percentage discount to a decimal by moving the decimal two places to the left: 40 % = 40.0 % = .40 {\displaystyle 40\%=40.0\%=.40} 40\%=40.0\%=.40. Multiply the original price by the decimal: 154.88 × .40 = 61.95 {\displaystyle 154.88\times .40=61.95} 154.88\times .40=61.95. Subtract the discount from the original price: 154.88 − 61.95 = 92.93 {\displaystyle 154.88-61.95=92.93} 154.88-61.95=92.93. So, the sale price of the television is $92.93.

Find the exact sale price of a camera that is 15% off. The original price is $449.95. Convert the percentage discount to a decimal by moving the decimal two places to the left: 15 % = 15.0 % = .15 {\displaystyle 15\%=15.0\%=.15} 15\%=15.0\%=.15. Multiply the original price by the decimal: 449.95 × .15 = 67.49 {\displaystyle 449.95\times .15=67.49} 449.95\times .15=67.49. Subtract the discount from the original price: 449.95 − 67.49 = 382.46 {\displaystyle 449.95-67.49=382.46} 449.95-67.49=382.46. So, the sale price of the camera is $382.46.

Estimate the sale price. A tablet is regularly $199.99. On sale, it is 45% off. Round the original price to the nearest ten. Since $199.99 is only 1 cent away from $200, you would round up. Calculate 10% of the rounded price. Moving the decimal one place to the left, you should see that 10% of $200.00 is $20.00. Determine the number of tens in the percent off. Since 10 × 4 = 40 {\displaystyle 10\times 4=40} 10\times 4=40, you know that there are 4 tens in 45%. Multiply 10% of the rounded price by the appropriate factor. Since the percentage off is 45%, you would multiply 10% of the rounded price by 4: $ 20 × 4 = $ 80 {\displaystyle \$20\times 4=\$80} \$20\times 4=\$80 Calculate 5% of the rounded price. This is half of 10%, which is $20. So half of $20 is $10. Add the remaining 5% to the discount. 40% is $80, and 5% is $10, so 45% is $90. Subtract the discount from the rounded price: $ 200 − $ 90 = $ 110 {\displaystyle \$200-\$90=\$110} \$200-\$90=\$110. So the estimated sale price is $110.