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# HW 3 - Eric Johnston MAED 310 HW 3 1 The Russian Peasant...

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Eric Johnston MAED 310 HW 3 1. The Russian Peasant Algorithm is simply another form of multiplication, only this time there is no long multiplication. This method merely consisting of doubling, cutting in half, and adding up. There are four rules/step involved that make this algorithm work. Step 1 : Write each number at the head of a column. Step 2 : Double the number in the first column, and halve the number in the second column. If the number in the second column is odd, divide it by two and drop the remainder. Step 3 : If the number in the second column is even, cross out that entire row. Step 4 : Keep doubling, halving, and crossing out until the number in the second column is 1. Add up the remaining numbers in the first column. The total is the product of your original numbers! The reason this works is because multiplying by 2 on one side, and by 1/2 on the other side. That is 2(1/2) = 1, so the overall product stays the same. For the case where you divide an odd number in column two and you “drop” a one, it seems to be lost but actually that remained in the first column since it was not crossed off. Since you are not changing the product but simply grouping them differently, this creates each grouped box to become smaller than before, but with an extra remainder group added on at the end. This is related to the Egyptian Method of Duplation because in the Egyptian method you start with a one in the first column and the

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HW 3 - Eric Johnston MAED 310 HW 3 1 The Russian Peasant...

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