The discount formula
Sale price = original price x (1 - discount as a decimal). To turn a percent into a decimal, divide by 100. A 25% discount becomes 0.25, so you pay 1 - 0.25 = 0.75 of the price. Your savings are the original price minus the sale price, which is the same as original price x discount as a decimal.
Worked example: 25% off $80
Start with the discount as a decimal: 25 / 100 = 0.25. Subtract from one: 1 - 0.25 = 0.75. Multiply by the price: $80 x 0.75 = $60. That is the sale price. Your savings: $80 - $60 = $20, or $80 x 0.25 = $20. Two more, worked the same way: 10% off a $45 item is $45 x 0.90 = $40.50, saving $4.50. A 15% discount on $120 is $120 x 0.85 = $102, saving $18.
The 10% shortcut for mental math
Ten percent of any price is the price with the decimal moved one place left: 10% of $80 is $8. From there you can build any common discount. Twenty percent is double the 10% figure ($16 off $80, so $64). Fifteen percent is 10% plus half of 10% ($8 + $4 = $12 off $80, so $68). Twenty-five percent is 10% doubled plus half of 10% ($16 + $4 = $20 off $80, so $60). This trick makes sale tags readable at a glance without a calculator.
Stacked discounts multiply, they do not add
When a store offers 20% off and an extra 10% off at the register, the discounts apply one after another. On an $80 item: $80 x 0.80 = $64, then $64 x 0.90 = $57.60. The combined saving is 28%, not 30%. The gap widens with bigger discounts: 50% off followed by 50% off is 75% total, not 100%. Anytime you see "take an extra X% off sale prices," run the multiplication, because the headline number always overstates the deal.
Sales tax comes after the discount
Retailers charge sales tax on the discounted price, not the original. At 8% tax, a $60 sale price costs $60 x 1.08 = $64.80 out the door. If you computed tax on the original $80 instead, you would expect $86.40 and overestimate what you owe. When you budget for a purchase, always apply the discount first, then the tax.
Reading sale signs like a skeptic
Sale signs are written to maximize excitement, not clarity. "Up to 50% off" means one item somewhere is 50% off and everything else is less; the average discount is far lower. "Was $120, now $84" is a 30% discount: ($120 - $84) / $120 = 0.30. Run that division whenever the percent is missing, because the sign omits it exactly when the number is unimpressive. "Save $25 on $100" is 25% off, but "save $25" on a $250 item is only 10%. Always convert the dollar saving back to a percent so deals are comparable.
When the tag shows what you pay, not what you save
Some tags say "pay only 75%" instead of "25% off." These are the same deal, just framed from the other side. To convert, subtract from 100: pay 75% means a 25% discount, pay 60% means 40% off. This framing is common in clearance, where "take an extra 40% off the ticketed price" means you pay 60% of the ticket. On a $50 ticketed price: $50 x 0.60 = $30. If a sign ever confuses you, convert to "what percent do I pay" first, then multiply.
Three mistakes that cost shoppers real money
First, adding stacked discounts instead of multiplying them, which we covered above. Second, confusing "percent off" with "percent of": 25% off means you pay 75%, but many shoppers hear 25 and multiply the price by 0.25, which gives the savings, not the sale price. Third, trusting the "was" price. A 40% discount off an inflated reference price can be worse than a 20% discount off an honest one. Track the actual selling price over time instead of trusting the tag.