Long division calculator

Long division breaks one big division into a string of small ones, a digit at a time. Take 7625 ÷ 25. 25 doesn't go into 7, so start with 76. 25 goes into 76 three times, so write 3 on top, above the 6. Three 25s are 75, and 76 take away 75 leaves 1.

Bring down the next digit, 2, to sit beside the 1: that makes 12. 25 doesn't go into 12, so write 0 on top and bring down the 5 as well, making 125. 25 goes into 125 exactly five times. Write 5 on top, and there's nothing left. The answer is 305.

Every step is the same four moves, in the same order: divide, multiply, subtract, bring down.

When the digits run out and something's still left, that's the remainder. 100 ÷ 7 is 14 remainder 2.

The remainder can also go over the number you divided by, as a fraction: 2 left over from dividing by 7 is 2/7, so 100 ÷ 7 is 14 2/7. The calculator simplifies it, so 100 ÷ 8 comes out as 12 1/2 rather than 12 4/8.

For a decimal, put a decimal point after the last digit, add zeros and keep going. Some divisions stop, like 3 ÷ 4 = 0.75. Others never do: 1 ÷ 3 leaves a remainder of 1 every time, so the 3s go on for ever. When a remainder comes round again, the calculator says the decimal recurs. It also says so when the repeat starts beyond the places shown. 1 ÷ 7 to 2 places is 0.14, but the digits 142857 go on repeating.

Long division needs a whole number to divide by. If it has a decimal point, move the point in both numbers the same number of places until it doesn't. 7.5 ÷ 0.25 becomes 750 ÷ 25, because multiplying both numbers by 100 doesn't change the answer. The calculator does this first and says so in the working. The remainder is then divided back down by the same amount. 7 ÷ 2.5 becomes 70 ÷ 25, which is 2 remainder 20. Divide 20 by 10, and the answer is 2 remainder 2. Check: 2 × 2.5 + 2 = 7.

The layout here, with the divisor outside a bracket and the answer on top, is the one used in English-speaking schools. It isn't universal. In Germany, Austria and Switzerland the sum is written as an equation, 7625 : 25 = 305, with the working below it; the calculator accepts the colon too. In France, Spain, Italy and Russia the divisor sits to the right of the dividend, behind a vertical bar, and the answer goes underneath it.

The method itself is old. The earliest printed example is from Italy in 1491, and the version in use now is credited to Henry Briggs, around 1600.

Ages 9 and up, about 30 minutes. Work one division on the board step by step, then have students solve a similar one on paper and check each line against the working shown above, not just the answer. Mistakes usually show up at the bring-down step.

Take it further: give a division with a remainder and ask for the answer three ways, as a remainder, a fraction and a decimal, then check all three with the calculator's settings.

In England, short division is taught in Year 5 and long division by a two-digit number in Year 6. Common Core has one-digit divisors in grade 4 (4.NBT.B.6), two-digit divisors in grade 5 (5.NBT.B.6) and the standard algorithm by grade 6 (6.NS.B.2).