How to divide one positive integer (the *dividend*) by another, smaller positive integer (the *divisor*), obtaining a non-negative integer quotient and a non-negative integer remainder:

**Step 1.** Represent the dividend in the horizontal margin and the divisor in the vertical margin.

**Step 2.** Place a counter on the largest number in the first column (farthest column to the right) that when multiplied by the divisor is less than or equal to the dividend.

**Step 3.** Multiply that number by the divisor and subtract the product from the dividend. Replace the dividend (in the horizontal margin) with this result, which will become the current dividend.

**Step 4.** Repeat steps 2 and 3 with the current dividend until you can no longer do so.

**Step 5.** The sum of the chips in the first column is the quotient. The current dividend is the remainder.

**Example:** That \(100\) divided by \(7\) results in a quotient of \(14\) and a remainder of \(2\) is illustrated below.

**Steps 1 and 2.** The dividend \(100\) is represented in the horizontal margin and the divisor \(7\) in the vertical margin. Since \(7\cdot 16 > 100,\) but \(7\cdot 8 \le 100,\) a counter has been placed on the 8-square in the right-hand column.

**Steps 3 and 4.** Since \(7\cdot 8 = 56,\) the current dividend is \(100-56 = 44,\) as represented in the horizontal margin. Furthermore, since \(7\cdot 8 > 44,\) but \(7\cdot 4 \le 44,\) a counter has been placed on the 4-square in the right-hand column.

**Step 4.** Since \(7\cdot 4 = 28,\) the current dividend is \(44-28 = 16,\) as represented in the horizontal margin. Furthermore, since \(7\cdot 4 > 16,\) but \(7\cdot 2 \le 16,\) a counter has been placed on the 2-square in the right-hand column.

**Step 4, continued.** Since \(7\cdot 2 = 14,\) the current dividend is \(16-14 = 2,\) as represented in the horizontal margin. Since \(7\cdot 1 > 2,\) we cannot continue.

**Step 5.** We conclude that dividing \(100\) by \(7\) results in a quotient of \(8 + 4 + 2 = 14\) and a remainder of \(2.\)

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