Mental Maths for Everyday Money
Most of the arithmetic an adult actually does is about money, and almost all of it is the same half-dozen shapes: a share, a tip, a discount, a unit price, a rate, a rough total. None of them need a calculator, and all of them are faster to sanity-check than to type in.
Splitting a bill
Between two, halve. Between four, halve twice. Between three is the only one people hesitate over, and the trick is to go via ten per cent.
A £87 bill between three: 10% is £8.70, so 30% is £26.10. Three lots of £26.10 is £78.30 — a little short, so nudge to about £29 each. Precise enough for a restaurant, and it took two steps.
For five, take a fifth by doubling and moving the point: £87 → 174 → £17.40 each. Dividing by five is always “double it, then divide by ten”.
Tips and service
Everything comes off ten per cent, which is a decimal point moved one place.
| You want | Do this | On £64 |
|---|---|---|
| 10% | Move the point | £6.40 |
| 20% | Double it | £12.80 |
| 15% | 10% plus half again | 6.40 + 3.20 = £9.60 |
| 12.5% | 10% plus a quarter of it | 6.40 + 1.60 = £8.00 |
| 5% | Half of 10% | £3.20 |
Discounts: work out what you pay, not what you save
Thirty per cent off means you pay seventy. Going straight to the price you will actually hand over is one step instead of two, and there is no subtraction to fumble.
A £45 coat at 30% off: 10% is £4.50, so 70% is £31.50.
The trap: stacked discounts do not add. Twenty per cent off, then a further ten per cent, is not thirty per cent off. You pay 80%, then 90% of that, which is 72% — a 28% discount. Shops are not being dishonest, but it is never quite the number it appears to be.
Which packet is cheaper
Unit price is the only honest comparison, and you rarely need it exactly — you need to know which side of the line you are on.
500g for £3.20 against 800g for £4.80. Per 100g that is 64p against 60p, so the big one wins, but only by about six per cent. Worth knowing before you carry it home.
A quicker route when the numbers are awkward: scale one to match the other. Two of the 500g packs is 1000g for £6.40; 800g at £4.80 scales to 1000g for £6.00. Same conclusion, no division by three-digit numbers.
Interest, roughly
For anything compounding, the rule of 72 tells you how long money takes to double: divide 72 by the annual rate.
- At 6%, doubling takes about 12 years
- At 8%, about 9 years
- At 3%, about 24 years
It runs the other way too, and this is where it earns its keep. A debt at 24% doubles in about three years. A card balance you are not really paying down is not sitting still.
Percentage rises and the mistake everyone makes
A salary of £34,000 rising 3%: 1% is £340, so 3% is £1,020, giving £35,020.
Now reverse it. A price is £120 after a 20% rise — what was it before? Not £96. Taking 20% off the new figure is a different sum from adding 20% to the old one. The original was 120 ÷ 1.2 = £100.
This is the single most common percentage error there is, and it turns up in salary talk, VAT and sale prices alike. If something went up by a fifth, it has to come down by a sixth to get back.
The habit that matters most
None of this is about replacing your phone. It is about having an expectation before you look at it, so that a mistyped figure looks wrong instead of authoritative. A number you did not predict is a number you cannot check.
The percentage techniques go deeper on the same ground, and Carry the One‘s Oh Wow Expert mode drills percentages against a clock.
More like this: all the mental arithmetic guides.