Long division by a one-digit number without a remainder
Division of larger numbers is difficult, so we use written forms.
The dividend in our example it is 1752 and the divisor is 8. We begin by determining whether the first digit of the dividend (here 1) is greater than or equal to the divisor (here 8). If so, we can divide these numbers. In our case, the first digit of the dividend is smaller than the divisor, so we must also use the second digit in the dividend. So we count how many times 8 fits into 17. We write 2 in the result and calculate the remainder. We multiply the divisor and the result (2×8=16), write the number 16 under 17 and subtract (17−16=1). This remainder must be less than the divisor.
To the remainder (1) we write another digit (5). Since 15 fits 8 only once, we write 1 in the result. We multiply this result again by the divisor (8) and subtract from 15.
We subtract and write another digit (2) to the remainder 7. We know that 8 fits into 72 exactly nine times, so we write 9 in the result and the remainder is 0. The result of the whole operation is 219. In division, we call the result the quotient.
Take a look at another example: 12008÷8
Sometimes it happens that two zeroes occur in the calculation (in our case the remainder after division was 0 and next digit was 0 as well). In this case we write 0 in the quotient and continue with the next number.
If there occurs dividend smaller than divisor (during calculation in the example below there is
Long division by a two-digit number without a remainder
Dividing by a two-digit number is the same as by one-digit number. At the beginning we have to look at the first two digits (33), since we can't fit a two-digit number into a one-digit number (sometimes it is necessary to look at the first three digits instead).Long division with a remainder
For written division with a remainder, we use the same method as for division without a remainder. In the example 531÷4, we gradually divide the digits from the dividend by the divisor. If we look at the last operation, we see that the division came out with a remainder of 3. We can write that the result of our example is 132 (and remainder is 3). However, it is possible to calculate the exact quotient (instead of using a remainder) by adding a decimal point and zeroes to the dividend (count further outside the set of integers). We would then write the next digits after the decimal point.
