Skip to story
ELI5 Yahaaa

Counting up, not taking away

How Do You Work Out Your Change?

Shopkeepers never subtract — they count forwards from the price to the note.

1 The price is£6.402 Count up: 60pmakes £73 Then £3 makes£10 — change is£3.60
Nobody does the subtraction. They walk up the number line.

  1. Step 1 of 5

    Taking away across zeros is hard.

    Subtracting?£10.00 − £6.40, withborrowingCounting up £6.40 → £7 → £10

    Ten minus six pounds forty needs borrowing twice, and borrowing is where mistakes live. Most people get it wrong in their head.

  2. Step 2 of 5

    Counting up uses friendly stops.

    1 Start at £6.402 Jump 60p to £73 Jump £3 to £10

    You jump to the next round number first, then to the next, then to the note. Every jump is an easy one.

  3. Step 3 of 5

    Then you add the jumps together.

    First hop60p, to reach £7Second hop£3, to reach £10

    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.

  4. Step 4 of 5

    The coins come out in the same order.

    1 Small changefirst2 Then the roundpounds3 The pilematches thehops

    A shopkeeper hands the small change first and the notes last, because that is the order the hops happened in.

  5. Step 5 of 5

    It works for any awkward subtraction.

    1 19872 → 1990 → 2020 →20263=3 + 30 + 6 = 39

    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

Change is worked out by counting up from the price in easy hops and adding the hops, never by subtracting.

Try it yourself

Ask someone for change from £20 on a £13.85 bill. Watch whether they count up or try to subtract.

Topics

Next tiny story