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MECHANICAL MULTIPLICATION The people of the kingdom of Clotheah are weavers of the finest cloth in many lands. With the fine cloth they make beautiful cloaks. The king appointed his daughter, Princess Clotheah, mistress of the sewing circles. One of her duties is to attend the great bazaar and buy thread to make the beautiful cloaks.
At the bazaar, thread is sold on single spools and in wraps of ten spools. Each cloak requires two wraps of ten spools plus one single spool of thread or twenty-one spools altogether. Princess Clotheah must buy thread for one village sewing circle and three farm sewing circles. For the village sewing circle she must buy enough thread to make ten cloaks and for each of the farm circles enough for one cloak Therefore the princess must buy enough thread for thirteen cloaks. So she will need twenty-one times thirteen spools of thread.
The digits of twenty-one are represented by the base beads of a triangle pushed to the left on abacus B.
2 2 The digits of twenty-one or represented by the base beads of a triangle pushed to the left on abacus B.
2 1 To represent thirteen, on abacus C, one, then three base beads are pushed to the left.
X 1 1 To represent thirteen, on abacus C, one, then three base beads are pushed to the left.
1 3 Then all four are pushed back to the right on abacus D
1 After a few simple manipulations, the columns of beads in the middle will represent the product of 21 times 3 and the product of 21 times 10. First push the 1 of 21 to the right.
When you touch the bottom bead of the adjacent column stop. As the arrow shows push the bead you touched on the rod above to the right.
When you touch the bottom bead of the next column stop. As the arrow again shows push the bead you touched on the rod above to the right
2 7 3 The answer is revealed to be 273. From left to right you have two hundreds, then six plus one tens and three ones. Note how the six and one are automatically position such that the bottom bead of the six is directly above the one to indicate the same place value.
1 X 3 Now that we know how to array the beads we can follow the mechanical process. Princess Clotheah first purchased thread for the three farm circles. She bought one times three single spools and two time three wraps. On abacus E one column of the right columns is pushed to the right leaving two columns. These columns represent sixty-three spools of thread.
2 1 X 3 The distributed columns represent 21 times 3.Now distributing the remaining column as indicated above will represent 21 times 1.
2 7 3 So next Princess Clotheah purchased thread for the village circle. She bought one times ten single spools and two times ten wraps. On abacus F one base bead from the left column is pushed to the right leaving two beads. These beads represent 21 times 10 spools of thread. Complete the mechanical process by adding the place value columns.
