Enter the number being divided (the dividend) and the number you’re dividing by (the divisor). You get the whole-number answer with its remainder, the exact decimal, and each bring-down, divide, multiply and subtract step you’d write out by hand.
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Long division breaks a big division into small steps, working left to right through the dividend. At each step you bring down the next digit, divide to see how many whole times the divisor fits, multiply back, and subtract to get what’s left over. For 1234 ÷ 7: 7 goes into 12 once (remainder 5), into 53 seven times (remainder 4), and into 44 six times (remainder 2), so 1234 ÷ 7 = 176 remainder 2.
The remainder can be written as a fraction of the divisor, giving the mixed number 176 2⁄7. Keep dividing past the decimal point, adding zeros, and you get the decimal 176.285714285714…, where “285714” repeats forever. A remainder that comes back a second time is the sign a decimal has started repeating.
You can check any answer with quotient × divisor + remainder = dividend: 176 × 7 + 2 = 1234.
In 1234 ÷ 7 = 176 r 2, 1234 is the dividend, 7 is the divisor, 176 is the quotient and 2 is the remainder.
Put the remainder over the divisor: 176 r 2 with divisor 7 becomes 176 2⁄7. To get the decimal, keep dividing: add a decimal point and zeros to the dividend and carry on bringing down digits.
Multiply both numbers by 10 (or 100, 1000…) until the divisor is a whole number, then divide as normal. 12.5 ÷ 0.25 becomes 1250 ÷ 25 = 50. The quotient is unchanged; the remainder is in the scaled units.
After the dividend runs out, each step’s remainder is less than the divisor, so only a limited number of remainders are possible. Once one repeats, the digits after it repeat too. Divisions only end when the divisor’s prime factors are just 2s and 5s (after simplifying).
The signs are handled separately: a negative divided by a positive gives a negative quotient. The remainder is shown as a positive number, and the check line confirms the answer adds back up to the original dividend.
