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How to Do Long Hand Division

Long hand division is a method of dividing large numbers systematically. Unlike short division, readers can examine the process to understand how the user obtained the answer. The larger number that you divide is the dividend while the smaller number that you divide with is the divisor. The answer at the end of the process is the quotient.

Instructions

    • 1

      Pick a number and pick a smaller number with which to divide it. For instance, 504 divided by 14.

    • 2

      Write down the divisor and draw a short vertical line on its right side. Write the dividend on the right side of the vertical line and draw a horizontal line above it.

      ------

      14| 504

    • 3

      Attempt to divide the first number in the dividend by the divisor (5 divided by 14). Write the resulting number on the horizontal line. If there are any remainders, ignore them for the moment. If the divisor is bigger than the first number then write 0.

      0

      -------

      14| 504

    • 4

      Multiply the divisor and the number you wrote on the horizontal line. Write the answer under the first number in the dividend and draw a horizontal line under it. Subtract this number from the first number in the dividend and write the answer under the horizontal line.

      0

      -------

      14| 504

      0

    • 5

      Bring the second number in the dividend to the right side of the answer from step 4. Divide this new number by the divisor. Write the answer on the right side of the number above the dividend. Ignore any remainders.

      03

      --------

      14| 504

      0

      -------

      50

    • 6

      Multiply the divisor by the new number above the dividend and write the answer under the number you divided. Draw a horizontal line underneath. Subtract the smaller number from the larger one and write the answer under the horizontal line.

      03

      -------

      14| 504

      0

      -------

      50

      42

      -------

      8

    • 7

      Continue this process to the last number in the dividend.

      036

      -------

      14| 504

      0

      50

      -------

      42

      -------

      84

      84

      -------

      0

      504 divided by 14 = 36

      If there are any remainders after subtracting the smaller number from the larger number, write it as a remainder on the horizontal line above the dividend. For instance, 601 divided by 10 = 6 r 1

      06 r 1

      -----------

      10| 601

      0

      -----------

      60

      60

      -----------

      01

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