This long division calculator divides any two numbers and shows the complete answer three ways: quotient with remainder, the exact decimal, and the division worked by hand-style steps.
Worked steps (whole-number part)
How Long Division Works
Long division is chunking with discipline: take the dividend’s leading digits, ask how many whole times the divisor fits, write that digit of the quotient, subtract the product, bring down the next digit, and repeat until nothing remains but a remainder smaller than the divisor. The remainder then either stays as “r” notation, becomes a fraction (remainder ÷ divisor — see our Decimal to Fraction Calculator for the reverse trip), or continues into decimals by appending zeros. Part of our Math Calculators collection.
Worked Example (Verified)
987 ÷ 12:
- 12 into 98 → 8 (8 × 12 = 96), subtract: remainder 2
- Bring down 7 → 27; 12 into 27 → 2 (24), remainder 3
- Answer: 82 remainder 3 = 82 3/12 = 82 1/4 = 82.25 exactly
- And the classic: 22 ÷ 7 = 3.142857142857… — the repeating decimal behind π’s famous approximation
Remainder, Fraction or Decimal — Which Answer Do You Need?
- Remainder form — sharing indivisible things (987 candies among 12 kids: 82 each, 3 left over). The remainder is information, not error.
- Fraction/mixed form — exactness for measurement and cooking: 82¼.
- Decimal form — money, science and anything feeding further calculations; choose decimal places to match the precision you actually have.
- Always sanity-check by multiplying back: quotient × divisor + remainder must rebuild the dividend (82 × 12 + 3 = 987 ✔).
Related Tools
- Decimal to Fraction Calculator
- Math Calculators — the full collection
Frequently Asked Questions
How do I do long division?
Divide the leading digits by the divisor, multiply, subtract, bring down the next digit, and repeat — the worked steps above demonstrate on your own numbers. Finish with a remainder, a fraction, or decimals.
What is the remainder in 987 ÷ 12?
3 — because 82 × 12 = 984, leaving 987 − 984 = 3. As a decimal the division continues to exactly 82.25.
How do I turn a remainder into a decimal?
Keep dividing: append a decimal point and zeros to the dividend and continue the same process (3 remainder → 30 tenths ÷ 12 = 2, remainder 6 → 60 hundredths ÷ 12 = 5 → 82.25, done).
Why do some divisions never end?
When the divisor has prime factors other than 2 and 5 (7, 3, 11…), the decimal repeats forever — 1/3 = 0.333…, 22/7 = 3.142857142857…. These are rational numbers wearing infinite decimals; fractions express them exactly.
What is the dividend and the divisor?
The dividend is the number being divided up (987); the divisor is the number you divide by (12); the result is the quotient (82) possibly with a remainder.
Is this long division calculator free?
Yes — free, instant, no sign-up.