Percentages.

Ten percent is one decimal-place shift. Fifteen is ten plus half-of-ten. Twenty is ten doubled. Every common tip lives one hop from the 10% anchor.

"30% off" tempts you to compute the discount and subtract — two steps, two error chances. Compute what you actually pay: 70% of price, in one move.

Markup is the bump on top of cost. Margin is the slice of the final price. A 50% markup is only a 33% margin — the denominators differ.

Sales tax is a single multiplier on the pre-tax total. 1 + rate, applied once. Splitting it into "find tax then add it back" is two roundings and one extra step you don't need.

Ten is the keystone — every drill builds from there. 5% is half. 20% is double. 1% is another decimal hop. If you can land 10% in under a second, the rest comes free.

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.

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.

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.

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.

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.

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.

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.

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.