Scope and assumptions
Grocery discount % = (original − sale) ÷ original × 100. Illustrative prices.
A 25%-off sticker feels like a win, right up until the 500 g pack next to it turns out to be cheaper per gram. Supermarket discounts are ordinary percentage arithmetic, but the shelf is engineered to make the percentage the most visible number and the unit price the least.
Knowing which one decides the deal is most of the skill.
The drop, measured against the old price
Discount % = (original − sale) ÷ original × 100
The denominator is the original price. Dividing by the sale price instead inflates the discount every time — a $4 → $3 cut is 25%, not 33%.
| Original | Sale | Discount |
|---|---|---|
| $4.00 | $3.00 | 25% |
| $2.50 | $2.00 | 20% |
| $6.00 | $4.50 | 25% |
The comparison that actually decides it
A discount tells you how much a pack fell. It says nothing about whether that pack is now the cheapest option:
| Pack | Price | Per 100 g |
|---|---|---|
| 200 g, tagged 25% off | $3.00 | $1.50 |
| 500 g, no tag | $6.00 | $1.20 |
The tagged pack still costs 25 cents more per 100 g. The percentage was true and irrelevant. Shelf labels usually print unit price in small type near the barcode — that's the number to compare, not the red sticker.
Multi-buys and BOGO arithmetic
"3 for $5" only means something against the regular price. At $2 each, three would cost $6, so the offer saves $1 — about 16.7% off the trio.
"Buy one, get one free" on two $4 items: you pay $4 for $8 of product, which is 50% off the pair, not a free item and not 100% off anything. That framing matters because a "50% off second item" offer is only 25% off the pair — half the saving, dressed in the same language.
Stacked discounts multiply rather than add. An extra 20% off an already-50%-off item leaves you paying 0.5 × 0.8 = 40%, so the total reduction is 60%, not 70%.
Where the shopping math goes wrong
Dividing by the sale price instead of the original; forgetting the ×100 and reading 0.25 as the answer; assuming a bigger pack means a better percentage without checking unit price; computing a multi-buy saving without the regular price as a base; trusting the sticker over the unit-price line; and adding stacked percentages instead of multiplying them.
FAQ
Is 50% off then another 20% off the same as 70% off? No. The discounts stack multiplicatively: 0.5 × 0.8 = 0.4, so you pay 40% — a 60% total reduction, not 70%.
Why does unit price beat the discount percentage? Because the discount is measured against each pack's own starting price. A 25%-off 200 g pack can still cost more per 100 g than an undiscounted 500 g pack.
How do I compare "3 for $5" against a 20% off tag? Convert both to price per item. "3 for $5" at a $2 regular price is $1.67 each; a 20% tag on $2 is $1.60 each — the percentage wins.
Do loyalty-card prices count as the discount base? Yes, use what you actually pay. If the shelf price is $4 and your card makes it $3, your real discount is 25% — the headline tag may say something else.
Sources: Khan Academy, Percent word problems; shopping guides.
Disclaimer: Illustrative. Actual prices vary by store. Informational only.
Sources and references
- Khan Academy — Percent word problemshttps://www.khanacademy.org/math