Abacus Math Program – Lesson 6 – Ten Pair Complement Addition Part 2

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Continuing from Lesson 5, we will look at a few more 10 pair complement addition examples. Again there are 5 possible 10 pair complements: 9-1, 8-2, 7-3, 6-4, 5-5. All of these pairs can be used in two ways. For example we can use the pair 9-1 where we are trying to add 9 by subtracting the complement 1. But we can also think of it in the reverse way as 1-9 where we are trying to add 1 by subtracting the pair 9. So the following examples will look at some of the reverse possibilities such as adding +1, +2, +3, +4.

Here is our 10 pair complement addition rule again:

In this example we start by adding 5 to the abacus on rod B. Next we add 4 to 5 on rod B by moving 4 lower beads to the bar with the thumb. The interim sum is 9. Next we add 1 to 9 on rod B but notice there are no available beads to add 1 so we need the 10 pair complement addition rule. First add 1 to the next rod left, rod A and then subtract 9, the 10 pair complement of 1, from 9 on rod B. The interim sum is now 10. Finally add 3 to 10 by adding 3 lower beads to rod B. The final sum on the abacus is 13.

In this next example we start by adding 8 to the abacus on rod B. Next we add 4 to 8 on rod B but notice there is only 1 available bead so we will need our 10 pair complement addition rule. First add 1 to the next rod left, rod A. Then add 4 to 8 on rod B by subtracting 6, the 10 pair complement 4, from 8. The interim sum is now 12. Next add 6 to 12 by adding 6 to 2 on rod B for an interim sum of 18. Lastly subtract 3 from 18 by subtracting 3 from 8 on rod B leaving the final sum of 15.

In this last example we start by adding 9 to the abacus. Next we add 3 to 9 but notice there are no available beads on rod B to add 3 so we will need to use the 10 pair complement addition rule. First add 1 to 0 on rod A. Next subtract the 7, the 10 pair complement of 3 from 9 on rod B. The interim sum is now 12. Next subtract 2 from 12 by moving 2 lower beads away from the bar with the index finger on rod B. The interim sum is now 10. Lastly add 8 to 10 by adding 8 to 0 on rod B for a final answer of 18.

Hopefully the examples in lesson 5 and lesson 6 have helped you fully understand adding with 10 pair complements. In the next two lessons we will explore subtraction with 10 pair complements which will be the exact inverse of the addition rule. Next up Lesson 7 Subtraction Part 1.