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Long Division Calculator That Shows Every Step
Divide any two whole numbers and see the working: the UK bus stop layout, the full long division ladder, the remainder, the fraction and the decimal.
La réponse en bref
This calculator divides one whole number by another and shows the full working: the UK bus stop layout with carried digits, the long division ladder with every multiplication and subtraction, a remainder, a fraction and a decimal. It detects recurring blocks rather than rounding them away, and it will not round a figure silently.
- Whole-number answer
- 788
- Remainder
- 0
Bus stop layout
This is how it is set out in a British classroom. The answer sits on top, and each remainder is carried as a small figure in front of the next digit instead of being written out as a subtraction — which is quick once the multiplication is secure, and impossible to follow when it is not.
Long division layout
0 7 8 8
--------
6 ) 4 7 2 8
- 4 2
-----
5 2
- 4 8
-----
4 8
- 4 8
-----
0The same division written out in full, the way most textbooks outside the UK set it out. Every multiplication and every subtraction gets a line of its own. It is slower, but it shows exactly where each figure came from, which is why it is the better one to learn on.
What to think at each step
- 16 will not go into 4, so write 0 above that figure and bring the next one down.
- 26 into 47 goes 7 times. 7 × 6 = 42, and 47 − 42 = 5.
- 36 into 52 goes 8 times. 8 × 6 = 48, and 52 − 48 = 4.
- 46 into 48 goes 8 times. 8 × 6 = 48, and 48 − 48 = 0.
Remainder as a fraction
The remainder is 0, so the division is exact and there is no fraction to write.
Every figure here is exact — nothing is rounded to make it fit
Setting the division up
Enter the number being divided and the number you are dividing by, then choose where to stop. "Stop at the remainder" gives the answer in the form a primary or lower secondary question asks for — 788 remainder 0, or 12 remainder 2. "Carry on into decimals" keeps going past the decimal point for as many places as you select, up to ten.
The dividend accepts up to ten digits and the divisor up to six, which covers every written-method question set at GCSE and well beyond. Both layouts, the step captions and the fraction form all redraw as you type.
The remainder form and the decimal form are shown together on purpose. They are the same division stopped at two different moments, and seeing 4728 ÷ 6 as both 788 exactly and 788.0 makes the relationship between them concrete.
Two layouts for the same sum
The bus stop is the British short form. Each remainder is carried and written as a small figure in front of the next digit of the dividend, so the whole division fits in two lines. It is fast, and it is what a UK pupil will be shown at school — but it hides the subtraction, so an error in it is very hard to trace.
The long division ladder writes the same steps out in full: the quotient digit above, the multiplication below the figure it came from, the subtraction line, and the next digit brought down. This is the layout used across most of the rest of the world, and it is the one worth writing out when a division goes wrong, because every intermediate number is on the page. Families with a child in a British curriculum school and a parent taught elsewhere are usually looking at both, which is why both are drawn here.
Underneath, each step is captioned with the sentence a pupil should be saying to themselves — including the awkward ones, where the divisor will not go and a zero has to be written in the answer before the next digit comes down. Missing that zero is the commonest reason a long division answer comes out with too few digits.
How a recurring block is found
Once the decimal point is passed, every step divides the previous remainder multiplied by ten. There are only ever fewer than d possible remainders when dividing by d, so a division that does not terminate must eventually reach a remainder it has already had. From that moment the digits it produces can only repeat.
This calculator watches the remainders rather than the digits. When one comes round a second time it stops, marks the repeating block with a line above it and says which remainder gave the game away. That is why 1 ÷ 6 is reported as 0.16 with the 6 recurring after two steps, rather than as 0.1666666667 after ten.
If ten decimal places pass without a remainder repeating and without the division finishing, the tool says the figure has been cut short. It does not round the last digit, because a rounded figure and an exact one look identical on the page and only one of them is worth marks.
What it will not do, and where pupils slip
It will not divide by zero, and it will not accept a negative or fractional divisor, because the written method is defined for whole numbers and the layout stops meaning anything without them. It also will not present a rounded decimal as an exact one — where the division has been cut short, it says so on the same line as the figure.
The two slips that cost the most marks are both about place value. The first is forgetting to write a zero in the quotient when the divisor will not go into the working figure, which silently shortens the answer by a digit. The second is losing the decimal point when the whole numbers run out, so a correct string of digits ends up ten times too big or too small.
The third is stopping at the remainder when the question wanted a decimal, or the reverse. Read the wording: "how many whole boxes" wants the remainder, "give your answer to 2 decimal places" does not, and "give your answer as a mixed number" wants the fraction form shown here.
Questions fréquentes
What is the bus stop method?
It is the short written form of division taught in British schools, named after the shape drawn around the dividend. The answer is written above the line and each remainder is carried as a small figure in front of the next digit, rather than the subtraction being written out underneath as it is in the long division layout.
How do you write a remainder as a fraction?
Put the remainder over the divisor and cancel. 50 ÷ 4 is 12 remainder 2, and 2 over 4 cancels by 2 to one half, so the answer is 12 and a half. This calculator shows the cancelling factor as well as the finished fraction.
How do you know if a decimal recurs?
Watch the remainders, not the digits. Dividing by d can only ever produce fewer than d different remainders, so if the division has not terminated, one must come round again — and from that point the digits repeat. This tool stops at that moment and marks the repeating block.
Why does the answer sometimes start with a zero?
Because the divisor did not go into the first figure of the dividend. Writing that zero above the line keeps every later digit in its correct column. Dropping it is the most common reason a long division answer comes out ten times too small.
Sources
- National curriculum in England: mathematics programmes of study — Department for Education
- Pearson Edexcel GCSE (9–1) Mathematics — specification — Pearson Edexcel
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