Soroban abacus and finger math

Have you ever wondered why the Oriental Soroban abacus has 4 separate beads? It is in base 10, not 4 or 5, so why organize it that way?

In response to yesterday’s post Hand tricks! Alexander Bogomolny linked his page explaining finger math. As I looked at that neat way of counting to 99 on your two hands, I finally understood Soroban! The four beads stand for the four fingers on your hand, and the separate bead for the thumb.

With Alexander’s photos of hands, and screenshots from an online Soroban abacus, I can show the idea. It works the best if you count along. First, use the four fingers of your right hand to count 1, 2, 3, 4. This corresponds to the four beads in the first row of Soroban, shown yellow.

Then things become slightly more abstract. The thumb stands for 5, all by itself, just like the lonely yellow bead does. We move from direct counting to symbols:

You add fingers to the thumb to count 6, 7, 8, 9. Imagine a young child playing traditional finger counting games with parents. Kids can instantly recognize (subitize) quantities from 1 to 4, but the Western finger counting goes all the way to 10 – well beyond the subitizing range. Unlike the Western finger counting, this system introduces groups and symbols (the thumb stands for 5), as well as addition, as soon as you leave the subitizing range.  In other words, the system follows the way children’s minds work.

What happens when you arrive at 10? Something very rewarding and exciting! You get to use your other hand, which stands for the new place value – and the new row of beads on the abacus. The digits, the beads, and the fingers all fit together like hand in glove.

Here is another difference of this system from just counting your 10 fingers. You can count all the way to 99 on your two hands!

And if you join forces with a friend, you can show even bigger numbers.

Here is a video showing how to count all the way from 1 to 99: