Long Division Calculator Widget
Show pupils long division the way it is written on paper. Enter a dividend and a divisor to get the quotient with its remainder, the exact decimal (repeating digits in brackets) and a step table that mirrors the bus-stop method line by line.
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<iframe src="https://a2z.tools/embed/w/long-division-calculator" title="Long Division Calculator by A2Z Tools" width="100%" height="600" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>
A plain iframe. Works everywhere, including site builders that strip scripts. Adjust height if your content needs more room.
<div data-a2z-widget="long-division-calculator" data-height="600"></div> <script async src="https://a2z.tools/embed.js"></script>
Adds a small script (what it does) that sizes the widget to fit its content, loads it lazily and keeps it isolated from your page's CSS.
Works with
How it works
The widget starts with the shortest leading part of the dividend that is at least the divisor - for 7485 / 12 that is 74 - and then repeats the four classroom moves: divide (74 / 12 = 6), multiply (6 x 12 = 72), subtract (74 - 72 = 2) and bring down the next digit (28). Each row of the table is one of those cycles and contributes one digit of the quotient, so 623 can be read straight down the first column. The remainder that is left is checked with quotient x divisor + remainder = dividend. For the decimal answer the division continues on the remainder times ten; if a remainder comes back that was seen before, the digits from that point repeat forever and are shown in brackets, as in 1 / 6 = 0.1(6) or 22 / 7 = 3.(142857). Cycles longer than 40 digits are cut short with an ellipsis. Whole numbers only: dividends up to 15 digits and divisors up to one billion.
Calculation method
- dividend = quotient x divisor + remainder, 0 <= remainder < divisor
- Each step: divide, multiply, subtract, bring down the next digit
- Decimals: keep dividing remainder x 10; a repeated remainder marks the repeating block
Worked examples
Bus-stop method
Inputs: 7485 / 12
Result: 623 R 9; decimal 623.75
74 / 12 = 6 r 2; 28 / 12 = 2 r 4; 45 / 12 = 3 r 9.
A repeating answer
Inputs: 22 / 7
Result: 3 R 1; decimal 3.(142857)
Remainders 1, 3, 2, 6, 4, 5 then 1 again, so six digits repeat.
Limitations
- Whole, non-negative numbers only; decimal divisors must be scaled first.
- The layout is a step table, not the drawn bracket of the paper method; regional layouts (European, Indian) differ in where the quotient is written.
- Repeating blocks longer than 40 digits are shown truncated with an ellipsis.
Where publishers use it
- Year 5 and Year 6 maths pages teaching the bus-stop method
- Homework-help sites where parents check a child's working
- Teacher resource pages that need worked examples to project in class
- Pages on recurring decimals and converting fractions to decimals
- Adult numeracy and exam-refresher courses
Questions
What is 7485 divided by 12 with remainder?
623 remainder 9, because 623 x 12 = 7476 and 7485 - 7476 = 9. As a decimal it is 623.75, since 9 / 12 = 0.75.
What do the brackets in 0.1(6) mean?
The digits in brackets repeat forever: 0.1(6) is 0.16666..., which is 1/6. 22/7 = 3.(142857) repeats a six-digit block.
How do I divide by a decimal such as 0.3?
Multiply both numbers by 10 until the divisor is whole: 7.5 / 0.3 becomes 75 / 3 = 25. The widget asks for whole numbers so the steps stay like the paper method.
What happens when the divisor is bigger than the dividend?
The quotient is 0 and the remainder is the dividend: 5 / 7 = 0 R 5, and the decimal 0.(714285) shows the rest.
Why is dividing by zero not allowed?
No number times 0 gives a non-zero dividend, so the answer is undefined. The widget asks for a divisor of 1 or more.
How is long division different from short division?
Short division writes only the carried remainders next to each digit and suits single-digit divisors such as 7. Long division writes out each multiply-and-subtract line beneath, which is easier to follow when the divisor has two or more digits, like 12 or 125.
What is the chunking or partial-quotients method?
Instead of one digit per step, you subtract convenient multiples of the divisor - 7485 minus 500 x 12, then minus 100 x 12, and so on - and add up the chunks. It reaches the same quotient, 623 remainder 9, and many primary schools teach it before the formal written method.
How can I tell in advance whether the decimal will stop?
Reduce the fraction first. If the denominator has no prime factors other than 2 and 5, the decimal terminates: 9/12 = 3/4 gives 0.75. Any other prime factor, such as the 3 in 1/6 or the 7 in 22/7, makes it recur.
Why does long division look different in other countries?
The steps are the same, but the notation varies. UK and US schools put the divisor outside a bracket on the left with the quotient above; much of continental Europe writes 7485 : 12 = 623 with the working underneath; parts of Latin America place the divisor in a corner bracket on the right.
Cite or recommend this tool
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A2Z Tools Long Division Calculator https://a2z.tools/embed/long-division-calculator
<a href="https://a2z.tools/embed/long-division-calculator">A2Z Tools Long Division Calculator</a>
[A2Z Tools Long Division Calculator](https://a2z.tools/embed/long-division-calculator)
Long Division Calculator by A2Z Tools - https://a2z.tools/embed/long-division-calculator
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