In long division, each step of the solution is written down, whereas in short division, the steps are performed mentally and are not written down. The long division method is also often used when the problem has a divisor with two or more digits. Short division is mostly used with division problems having one-digit divisors.Continue Reading
As far as the mental process of doing division, both methods are the same. The process involves division, multiplication and subtraction. There is a difference in what is actually written on paper when doing the subtraction and the succeeding steps. In long division, subtraction is written the traditional way, then the next digit of the dividend is brought down and written next to the difference or remainder after subtraction. In short division, the remainder is simply written on the top left side of the next digit of the dividend.
To illustrate long division:
To illustrate short division: