Converting with a rate goes one way; the return trip divides. Multiplying when you should divide — with currencies, per-capita figures or any 'per' rate — produces an answer that's the right shape and completely wrong.
A rate like 1.25 $/£ carries its direction in tiny print. Both directions feel like 'using the rate', and the inverted result is rarely absurd enough to self-expose.
Write the rate as a fraction with units (1.25 dollars per 1 pound) and cancel units like algebra: pounds × (dollars/pound) leaves dollars ✓. If your units don't cancel to the thing you want, you're holding the rate upside down. Estimate to confirm direction: more dollars than pounds, fewer pounds than dollars.
Region A: £3.9m over 15 stores. Region B: £2.0m over 9 stores. What were the higher region's sales per store?
Convert each series to the same per-unit rate (value ÷ count) before comparing — never compare raw totals. The correct answer is £260k. Traps to avoid: £433k comes from the "cross divide" error; £222k comes from the "absolute not per store" error; £133k comes from the "cross divide" error; £246k comes from the "pooled" error.
This trap appears in 55 of our questions, across: Rate comparison · Per-capita rate · Currency conversion · Currency with commission.
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