Percentages

A word problem shows up — something like "What's 15% tip on $48?" or "$72 with 20% off. Final price?". Type the dollar answer on the keypad or your keyboard. Use the . key for cents when you need them. The moment your input matches the correct number, the next problem loads — no submit button to hit. Enter also force-submits. Press Space to skip. One shot per problem: if the answer is wrong, the correct value flashes, the miss gets logged in the margin, and the next problem takes over. Pick which percentage types show up and how messy the rates get from the start panel.

Percentages feel harder than they are because schools teach them algebraically. In real life — at a restaurant table, in a checkout line, reading a sale tag — you never "set up an equation." You break the number into pieces you already know, add or subtract, and you're done. These are the moves that will get you fast.

How do I calculate a tip in my head?

Find 10% first, then build up to whatever tip you want. 10% of any dollar amount is just the same number with the decimal moved one place to the left. Once you have 10%, every other common tip is a tiny adjustment from there.

Walk through a 20% tip on a $48 bill:

1. 10% of $48 is $4.80 (move the decimal one left).
2. 20% is just double: $4.80 + $4.80 = $9.60.
3. Leave $9.60 on the table. Done.

Same trick on a $63 bill at 20%: 10% is $6.30, double it to $12.60. The whole calculation takes about two seconds once the pattern clicks.

What's the trick for a 15% tip?

15% = 10% plus half of 10%. Find 10% the easy way, then add half of that number to itself. The halving is the only mildly tricky bit, and it's easier than it looks because you're only halving a small number.

Walk through 15% on a $42 bill:

1. 10% of $42 is $4.20.
2. Half of $4.20 is $2.10.
3. Add: $4.20 + $2.10 = $6.30. That's the 15% tip.

How do percentages work for a discount?

A "20% off" sign means you're paying 80%. That reframe alone saves most people a step. Find 80% of the price directly instead of calculating the discount and subtracting.

Walk through a 20% discount on a $72 jacket:

1. 10% of $72 is $7.20.
2. 80% means eight of those: 8 × $7.20 = $57.60.
3. Or, equivalently, $72 − ($7.20 × 2) = $57.60.

Both paths land in the same place; pick whichever feels faster on a given number. The trickier discounts are the "extra 25% off already reduced" signs — those don't stack. 50% off then 25% off isn't 75% off; it's 50% × 75% = 37.5% of the original. Walk the discounts one at a time, on the current price, and you'll stay out of trouble.

How do I figure out sales tax without a calculator?

Sales tax is just a tip by another name — you're adding a percentage to a subtotal. The only twist is that the rate is usually a weird number like 7% or 8.875%. The 10%-first trick still does most of the work.

Walk through 7% tax on a $60 subtotal:

1. 10% of $60 is $6.00.
2. 7% is 70% of that: $6.00 × 0.7 = $4.20.
3. Total: $60 + $4.20 = $64.20.

For 6% tax, same move, times 0.6. For 8%, times 0.8. Once you internalize that "find 10%, then scale," every whole-number tax rate under 10% takes the same amount of effort.

Is there a fast way to do 8.875% or 6.25% tax?

Round the rate, estimate the total, then adjust at the penny level if you need exact. For mental math at a checkout, you almost never need the last penny — you need to know whether the total will be $64 or $94. Treat 8.875% as "a bit under 9%" and 6.25% as "a quarter above 6%," and you'll land within a dime on any normal purchase.

Walk through 8.875% on $50 (NYC sales tax):

1. Round the rate to 9% for a quick estimate.
2. 9% of $50 = 10% ($5) − 1% ($0.50) = $4.50.
3. Real answer is a touch lower. $4.44 is exact, but $4.50 is close enough to sanity-check a receipt.

For 6.25% on $80: 6% is 60% of 10%, so $8 × 0.6 = $4.80. Add a hair for the extra 0.25% — $80 × 0.0025 = $0.20. Total tax is $5.00 and the full bill is $85.00. If that feels like too many moves, just round to 6% — you'll be off by twenty cents on an $80 purchase, which nobody at the register is auditing.

How do I figure out a markup or a price increase?

A markup is a discount run in reverse. "15% markup" means the new price is 115% of the old price. Same 10%-first move works: find 10%, scale to 15%, add to the original.

Walk through a 15% markup on $40:

1. 10% of $40 is $4.00.
2. 15% is $4.00 + half of $4.00 = $6.00.
3. New price: $40 + $6.00 = $46.00.

Same structure applies to a salary raise, a rent increase, or a contractor's "plus 20% materials" line item. Find the piece, add it on.

Why is 10% the one percentage I should memorize cold?

Because every other common percentage is built from 10%. 5% is half of 10%. 15% is 10% plus half. 20% is double 10%. 25% is double-and-a-bit. Every tip, every sale tag, every tax rate — all of them live within arm's reach of the 10% number, which you get for free by sliding a decimal point one place to the left. Make this one move automatic and percentages stop being a category of math that requires thought at all.

The register does the math for me. Why bother?

Three reasons. First, you catch mistakes — tips get entered on the wrong line, sale signs lie about what stacks with what, tax gets applied to items that should be exempt. Second, you make faster decisions — "is 30% off $180 cheaper than 25% off $175?" is a five-second question for someone fluent and a stop-and-think moment for everyone else. Third, you stop outsourcing a small but daily piece of judgment — and the ripple effect on everything from grocery shopping to negotiating a raise is larger than you'd expect.

Related drills on Practice

Quick Math trains the addition-and-multiplication fluency that every percentage shortcut relies on. Making Change shares the same "work in cents" mental model — once you can split a dollar into pieces, tips and sales tax become the same move in a different outfit. Tape Measure trades cents for sixteenths but uses the same "find the nearest landmark, then adjust" trick you've been building here — handy for a 10% material overage estimate on a cut list.

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• Tip calculator card A credit-card-sized reference you keep in your wallet. Belt-and-suspenders while you're building the habit — and no one ever notices you glance at it.
• Mental math tricks book Arthur Benjamin's "Secrets of Mental Math" has the best percentage chapter going. Cheap, readable, the moves actually stick.
• Cash-envelope wallet If you're practicing percentages because you're getting serious about a budget, a cash envelope system makes every discount and tax hit feel physical — and mental math is the only way to stay ahead of it at the register.