The error, demonstrated
A $270.74 total at 8.25% tax. Subtract 8.25% and you get $248.38. The correct pre-tax figure is $250.10 — because $270.74 ÷ 1.0825 is the only operation that undoes × 1.0825. The subtraction error grows with the rate: at 8.25% it is $1.72 on this receipt, $86 on a $12,000 invoice — enough to fail an audit line.
Why the brain wants to subtract
"Take off 8.25%" is a phrase about percentages of the thing in front of you. But the tax was computed on a smaller, hidden number — the pre-tax price. Undoing an addition requires division; the intuition that says "subtract" is answering a different question ("what is 8.25% of the total?"). Naming the intuition is half the fix; the calculator is the other half.
Where this matters in real life
Expense reimbursements (policies that say "pre-tax" while receipts show totals), sales commissions on tax-included revenue, VAT reclaim for travelers, and margin math for resellers — each is a place where the subtraction error quietly costs money monthly. Divide. Bookmark the calculator. Move on.