A NOTE ON LONG DIVISION

HAROLD D. LARSENThe University of New Mexico, Albuquerque, New Mexico

The process of long division is usually considered to be one of the mostdifficult operations in arithmetic. Much of this difficulty is due to the in-sistence on finding the correct quotient figure before proceeding with thedivision. This frequently requires two or more trials and the consequenterasures of the discarded products. Elaborate rules have been formulatedto aid in determining the correct quotient figure, all of which require con-siderable mental computation.As a matter of fact, the difficulty of long division has been exaggerated.

The whole process is very much simplified if an incorrect product is noterased. If the subtraction of the trial product is actually carried out, theremainder can be used very conveniently to adjust the incorrect quotientfigure. I have examined a large number of text-books on arithmetic, buthave failed to find any discussion of such adjustments.The following examples illustrate simple methods for adjusting trial

quotients. Two cases arise, depending on whether the trial quotient is toosmall or too large.Example 1. Explanation. The trial quotient 7 yields a re-

8 mainder 648, and hence is too small. Instead of71 erasing the trial product and starting over, it

��� is more convenient to change the quotient582)47223 figure to 8 by subtracting an additional 582 from

4074 648.

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Example 2. Explanation. The trial quotient 8 is too large,7 since the trial product exceeds the dividend by^6 118. Change the quotient figure to 7 by adding

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