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Sharing, with an awkward remainder

How Do You Split a Bill Fairly?

Dividing a bill is easy until it does not divide, and then it becomes a question about people.

12 counters Starting total ÷ 4 GROUP 1 GROUP 2 GROUP 3 GROUP 4 4 equal groups · 3 in each
Twelve pounds between four is the easy case. Most bills are not.
  1. Step 1 of 5

    An even split is just division.

    1 £60 total2 Four people3 £15 each

    The total divided by the number of people. Sixty between four is fifteen each, and nobody argues.

  2. Step 2 of 5

    Most bills do not divide neatly.

    Divides £60 ÷ 4 = £15 exactlyDoes not?£61 ÷ 4 = £15.25 —round up or down?

    £61 between four is £15.25. Real bills leave pennies, and pennies cannot be cut, so somebody has to absorb them.

  3. Step 3 of 5

    Rounding up is the usual answer.

    1 £15.25 each2 Round to £163 £64 collectedon a £61 bill

    Everyone pays the next round amount and the extra covers the remainder, and usually part of the tip too.

  4. Step 4 of 5

    Itemising is fairer and much slower.

    Even split Fast, slightly unfairItemised Fair, slow, and awkward

    Paying for what you ordered is exactly right and takes ten minutes. Splitting evenly is roughly right and takes ten seconds.

  5. Step 5 of 5

    The maths is easy; the choosing is not.

    The billSpeed andgoodwillExactness

    Arithmetic tells you every possible answer. Which one a table picks is about who ordered the wine, and no sum settles that.

    Splitting by rounding everyone up is also the only method where the total collected is never short.

The short version

Splitting a bill is division until the remainder appears, and then it stops being arithmetic and becomes a decision.

Try it yourself

Split a £47 bill three ways. Notice how quickly you reach for £16 each rather than £15.67.

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