Using the calculator
Type the sum as the number you're dividing, then ÷ or /, then the number you're dividing by: 7625 ÷ 25 or 7625 / 25 both work, and so does 7625 divided by 25. The answer appears as you type, with the written method drawn underneath and each step explained in words.
Answer as picks how anything left over is written. Remainder gives 14 remainder 2, fraction gives the mixed number 14 2/7, and decimal carries on past the decimal point to the number of places you choose, rounding the last one.
Put one sum on each line to do several at once. The working is shown for the first.
How long division works
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.
Remainders, fractions and decimals
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.
Dividing by a decimal
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 same sum, written around the world
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.
Questions
What are the dividend, divisor and quotient?
In 7625 ÷ 25, 7625 is the dividend, the number being divided. 25 is the divisor, the number you divide by. 305, the answer, is the quotient.
Why is there a 0 in the answer?
When the divisor doesn't go into the number you've reached, you write 0 above that digit and bring down the next one. Leaving the 0 out would shift every digit after it into the wrong place, turning 305 into 35.
How do I check the answer?
Multiply the answer by the divisor and add the remainder. You should get back the number you started with: 14 × 7 + 2 = 100.
Can I divide a negative number?
Divide without the signs, then put a minus in front of the answer if exactly one of the two numbers was negative.