Smart Shopping Math: Discounts, Tips, Sales Tax and Splitting Bills
How to work out real sale prices, stacked discounts, tips and shared bills with clear examples and quick mental shortcuts.
Sale prices in your head
To find a price after a discount, subtract the discount from 100 and multiply by the rest. 30 percent off is 70 percent of the price, so a 90 jacket costs 90 × 0.7 = 63. Another route: find 10 percent (9), multiply by three (27), and subtract from the price (63). Both give the same answer, and the second is easy to do mentally. The Discount Calculator confirms the result and shows your savings.
Why stacked discounts are smaller than they look
Two discounts are applied one after the other, each to the new price. 20 percent off, then another 10 percent off, leaves 0.8 × 0.9 = 0.72 of the price, which is a 28 percent total discount, not 30. Three stacked 10 percent discounts give 0.9 × 0.9 × 0.9 = 0.729, or 27.1 percent off. When a store advertises an 'extra 25 percent off sale prices', calculate from the sale price, not the original.
'Buy one, get one half price' on two items equals 25 percent off the pair. 'Buy two, get one free' on three equal items equals 33 percent off.
Sales tax and VAT
If tax is added on top, multiply by one plus the rate: with 8 percent tax, a 50 item costs 50 × 1.08 = 54. If a price already includes tax, divide to remove it. For a price of 118 with 18 percent tax included, the pre-tax price is 118 ÷ 1.18 = 100, and the tax is 18. Subtracting 18 percent of 118 would give the wrong answer (96.76).
Tipping
Customs differ widely. In the United States, 15 to 20 percent of the pre-tax bill is typical in restaurants. In many countries, a service charge is already included, and tipping is optional or a small round-up. Check your receipt before adding a tip so you do not pay twice. To tip quickly: find 10 percent by moving the decimal point, then double it for 20 percent or add half of it for 15 percent. The Tip Calculator handles the total and each person's share.
To split a bill fairly when people ordered very different amounts, work out each person's items first, add a share of shared dishes, tax and tip in proportion, instead of dividing the total equally.
Unit prices and real comparison
A bigger pack is not always cheaper per unit. Divide the price by the amount: a 500 g pack at 2.50 costs 0.50 per 100 g, while a 750 g pack at 3.45 costs 0.46 per 100 g. Shops often display a unit price on the shelf label. Compare like with like, and consider whether you will use it all before it expires. The Percentage Calculator helps you find how much cheaper one option is than another.
A quick checklist before you buy
Find the final price including tax and delivery. Compare unit prices. Check whether a discount is applied to the original or sale price. Ask whether the 'original' price was ever real. And decide whether you would buy the item at the sale price if the sale did not exist.