How do you calculate a discount in your head?

Anchor on 10 percent, which is the price with the decimal moved one place left. On a $45 item, 10 percent is $4.50. Multiply for the discount you need: 30 percent off is three of those, $13.50, leaving $31.50. For 25 percent, take a quarter, which is halving twice. For 15 percent, take 10 percent plus half of it. Alternatively, calculate what you pay rather than what you save, since 30 percent off means paying 70 percent, and multiplying by 0.7 is one step instead of two.

The stacking rule catches people and costs money. Discounts applied in sequence multiply rather than add, so an extra 20 percent off an already 20 percent reduced price is not 40 percent off. The first cut leaves you paying 80 percent, and the second leaves you paying 80 percent of that, which is 64 percent, meaning a 36 percent total discount. The same arithmetic works in reverse and explains why a price cut of 50 percent followed by an increase of 50 percent leaves you below where you started, at 75 percent of the original.

Two adjacent calculations worth knowing. Percentage off and percentage markup are not symmetric: a retailer marking up cost by 50 percent has a margin of 33 percent, not 50, because markup is calculated on cost while margin is calculated on price. And for comparing deals, unit price is the number that settles it, which is why unit pricing on shelf labels is required in many jurisdictions and worth reading, since larger packages are not reliably cheaper per unit despite the assumption. Finally, treat percent-off framing skeptically against a reference price you cannot verify, because a discount from an inflated original is the oldest pricing tactic there is and is regulated as deceptive when the reference price was never genuinely charged.