Counting up, not taking away
How Do You Work Out Your Change?
Shopkeepers never subtract — they count forwards from the price to the note.
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Step 1 of 5
Taking away across zeros is hard.
Ten minus six pounds forty needs borrowing twice, and borrowing is where mistakes live. Most people get it wrong in their head.
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Step 2 of 5
Counting up uses friendly stops.
The stop is picked because it is easy to reach, not because it is halfway You jump to the next round number first, then to the next, then to the note. Every jump is an easy one.
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Step 3 of 5
Then you add the jumps together.
The change is not the distance you measured — it is the sum of the hops you took. Sixty pence plus three pounds is three pounds sixty.
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Step 4 of 5
The coins come out in the same order.
Small coins first, then the pounds. The pile arrives in the order you hopped. A shopkeeper hands the small change first and the notes last, because that is the order the hops happened in.
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Step 5 of 5
It works for any awkward subtraction.
Working out 2026 minus 1987 is the same trick: hop to 1990, then to 2020, then to 2026. Thirty-nine years, no borrowing.
This is why old shopkeepers could give change faster than a till, and why they said the numbers out loud.
The short version
The change is not the distance but the sum of the hops, which is why the coins come out small first — that is the order the hops happened in. The same trick handles 2026 minus 1987: hop to 1990, then 2020, then 2026, and never borrow.
Try it yourself
Ask someone for change from £20 on a £13.85 bill. Watch whether they count up or try to subtract.