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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.
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.
In cases where one or more of the b terms has more than two digits, the final quotient value b cannot be constructed simply by concatenating the digit pairs. Instead, each term, starting with b 1 , {\displaystyle b_{1},} should be multiplied by 100, and the next term added (or, if negative, subtracted).
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To divide 46785399 by 96431, the bars for the divisor (96431) are placed on the board, as shown in the graphic below. Using the abacus, all the products of the divisor from 1 to 9 are found by reading the displayed numbers. Note that the dividend has eight digits, whereas the partial products (save for the first one) all have six.
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