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Abacus

 

 

The exact date of the development of this device is uncertain, as is the country of origin. It is generally believed that the abacus originated in China approximately 3000-5000 years ago. An example of its use is presented below. 

Ø Zero the registers by pushing all the beads away from the center bar. 

Ø Set the number 85607. The seven in the most right column. The 0 in the second column, the 6 on the third column, the 5 on the fourth and the 8 on the fifth column from the right. The seven will be indicated by pushing one bead of the upper portion and two beads of the lower portion to the center bar. The bead of the upper portion represents a 5 and the two beads of the lower portion represents 1+1 = 2. Together this will make 7. The 6 in the third column from the right can be ma de with 5 + 1 and the 8 with 5 + 1 + 1 + 1 (one bead of the upper portion and three of the lower portion).  We split the addition of 439 in an addition with 9, 30 and 400. 

Ø Add a 9 to the right column. We can split the 9 as 5 + 1+1+1+1. First add the 5 with a bead of the upper part. By doing this we can read the result 5+5 + 1+1 = 12 in this column. This is more than 9 and so we reduce this column with 10 (5+5) and add 1 on the second column from the right. After that we can add 1+1+1+1 at the most right column by moving the beads of the lower portion one by one to the center bar. After three beads all the beads of the lower part are moved to the center bar and we can not add the last bead. We can even the five beads of the lower portion with one bead of the upper portion (move the beads of the lower portion away from the center bar and move one bead of the upper portion to the center bar). Finally we add the last bead by moving one bead of the lower portion back to the center bar again. We can read the result of 85607 + 9 = 85616. 

Ø Add 30 by adding 3 at the second column from the right. In this case we can move 3 beads of the lower portion to the center bar. 

Ø Add 400 by adding 4 at the third column from the right. Move 4 beads of the lower portion to the center bar. The result in this column is 10. Zero this column and add 1 add the fourth column from the right.  Read the result: 86046.