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In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. [1]
Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size of the divisor. [1] For instance, suppose each egg carton fits 12 eggs, and the problem is to find how many cartons are needed to fit 36 eggs in total. Groups of 12 eggs at a time can be separated from the main pile until none are left, 3 groups:
Next one repeats step 2, using the small digit concatenated with the next digit of the dividend to form a new partial dividend (15). Dividing the new partial dividend by the divisor (4), one writes the result as before — the quotient above the next digit of the dividend, and the remainder as a small digit to the upper right.
More systematically and more efficiently, two integers can be divided with pencil and paper with the method of short division, if the divisor is small, or long division, if the divisor is larger. If the dividend has a fractional part (expressed as a decimal fraction ), one can continue the procedure past the ones place as far as desired.
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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
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