Q:

What is the difference between short and long division?

A:

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.

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:

  • Divide 252 by 7.
  • With long division, the first step is to divide 25 by 7.
  • Write 3 above the division bar over 5.
  • Next, multiply 7 by 3 and write 21 below 25.
  • Subtract 21 from 25 and write 4.
  • Bring down the next digit (2) of the dividend and write it beside the remainder 4.
  • Now, divide 42 by 7 and write 6 above the division bar over 2.
  • After multiplying 7 by 6 and subtracting 42 from 42, there's no remainder, so the quotient is 36.

To illustrate short division:

  • The first step is to divide 25 by 7.
  • Write 3 above the division bar over 5.
  • Next, mentally multiply 7 by 3, then subtract the product (21) from 25 and write the difference (4) on the top left side of the next digit of the dividend (2).
  • Now, divide 42 by 7 and write 6 above the division bar over 2.
  • Mentally multiply 7 by 6, then subtract the product (42) from 42.
  • Without any remainder, the quotient is 36.

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