Long division calculator with steps, plus long multiplication, addition and subtraction

If the number after bringing down is still smaller than the divisor, it cannot be divided: you write 0 in the quotient and bring down the next digit. It looks as if two digits came down together, but the zero in the quotient is essential. Take 6120 ÷ 6: after 6 − 6, bring down 1 — that is less than 6, so write 0 in the quotient and bring down 2: 12 ÷ 6 = 2. The answer is 1020; without the zero it would be 102, ten times too small.

From the first partial dividend. The first quotient digit goes over its last digit, and every remaining digit of the dividend adds one more digit to the quotient. In 1234 ÷ 56 the first partial dividend is 123 and one digit is left after it, so the quotient has two digits. It is a handy self-check: if you end up with more or fewer digits, a zero was skipped somewhere.

First make the divisor a whole number: move the decimal point to the right in both the divisor and the dividend by the same number of places. The quotient does not change, because both numbers were multiplied by the same power of ten. 12.5 ÷ 0.25 becomes 1250 ÷ 25, and you divide as usual. If the dividend runs out of digits, write zeros.

When the digits of the dividend run out, you write a zero next to the remainder and keep dividing. There are fewer possible remainders than the divisor, so sooner or later a remainder repeats — and from that point the quotient digits go around in a circle. The repeating block is marked with a bar in the US (0.3̅), with dots in the UK and Korea, and in parentheses in Russia: 0,(3). A decimal ends only when the reduced denominator has no prime factors other than 2 and 5.

The algorithm is the same everywhere; only the layout changes. In the US, UK, Korea and Indonesia the divisor sits to the left of a bracket and the quotient above the dividend. In Russia and Ukraine it is a corner, with the quotient under the divisor on the right. In Germany it is written in one line, "7854 : 6 = 1309", with the subtractions below, and in France the potence line runs the full height of the working. The Notation switch shows the problem exactly as a teacher in that country expects it.

The trailing zeros are set aside: write 2300 × 45 so that 23 stands over 45 and the two zeros stick out on the right. Multiply 23 by 45 to get 1035 and attach both zeros: 103,500. When a zero is in the middle of the multiplier, as in 305 × 204, the row of zeros is skipped and the next partial product is shifted two places at once (with two placeholder zeros in the US method).