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The Chinese Abacus 5

Addition 2

Larger Numbers

After doing the excercises in Page 4, you will have by now got a good grasp of the basic manipulation techniques for addition. For numbers with a longer string of digits, the processes are just the same, starting from the left and proceeding to the right.

86452 + 9621 = ?????

As usual if there is a smaller number to be added, then this should be the first number to be stacked into the abacus. In our example here, we will stack in 9621 first and then add 86452, ie,

9621 + 86452 = ?????


Other than noting that 8 is an order of magnitude greater, so it is stacked one rod to the left of the highest place of 9621, there are no surprises here.


Here we note that to enter the next digit in 86452, (i.e. 6), we have to think of 6 as being 10 - 4. That is stack in one 10's bead and withdraw 4 unitbeads.


The next digit in 86452, is 4, we have to think of this as being 10 - 6. That is, stack in one 10's bead and withdraw a topbead worth 5 and a unitbeads worth 1.


The next digit in 86452, is 5, we only have to stack in a topbead worth 5.


The last digit in 86452, is 2, only requires us to stack two unit beads towards the crossbar.



Notes

Notice that the numbers are constantly revised to take account of numbers greater than the current base 10 position. We say in the second move that adding the next number required the addition of a bead to the left of the current rod. This updated the 8.... to 95...

Exercises

Try adding 123456789 repeatedly to itself nine times. (You should get 1111111101 as an answer. You can ignore the advice of putting in the smaller number first, since that was just for getting you used to entering from the left to right, since the answer at each stage is larger than the number 123456789 to be added.)

Just to check, the answer at each stage is :

  1. 123456789
  2. 246913578
  3. 370370367
  4. 493827156
  5. 617283945
  6. 740740734
  7. 864197523
  8. 987654312
  9. 1111111101

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© Dylan W.H.Sung 1996-onwards
This page was created on Sunday 28th June 1998. It was recently updated on Monday 22nd April 2002