Chinese Abacus (算盘) vs. Japanese Abacus

[Altair]

I have read some books on the Japanese abacus (算盘) and know the basics of how to do calculations. Each rod of the Japanese abacuses I own have four unit-beads and one five-bead. I also own a Chinese abacus, which has five unit-beads and two five-beads on each rod.

I can do calculations on the Chinese abacus based on the methods I learned for the Japanese abacus; however, I cannot figure out a use for the fifth unit-bead or the second five-unit bead. If I use complementary numbers to do addition and subtraction, I would never use all five unit-beads to form the number five or both of the five-beads to from the number ten. Using all the beads on the rod to form the number 15 would be completely out of the question.

I found an excellent site (http://members.aol.com/chineseabacus/to_teacher.html) that talks about the Chinese abacus, but it does not explain uses for the extra beads.

Can anyone help with an explanation?

[Claw]

The extra unit-bead and five-bead are redundant. Technically speaking, if there was ever the case where you move all 5 unit-beads down, you would move them back up and move down one five-bead. Similarly, if you move all 2 five-beads down, you would move them back up and move down a unit-bead in the next column.

I guess this is useful for visualization of how the numbers are carried over, but the extra steps could be skipped once you know the rules. So the extra unit- and five-bead aren't really all that necessary in practice.

[Altair]

Thanks for the explanation. This makes sense. I have considered introducing my kids to the abacus and your response gives me the idea that the extra beeds might be helpful in teaching which numbers are complementary to which.