By the Beads

Q: Dear 100 HB:

How do you use an abacus?

Signed,

Calculator Challenged

A: Dear Antiquity Minded Mathematician

The 100 HB did not know how to use an abacus before this question, and it did take some time to understand the fundamentals of abaci usage. First off, abacus is a Middle English version of a Latin word abax (calculating table). But it is thought to come from Hebrew and Phoenician words for dust. However, the abacus has developed in parallel in multiple cultures, with some in the Middle East, Asia and Europe. The Russian version most know has parallel, horizontal strings with beads of different colors. The Chinese version - most often used now - has vertical strings with an upper section used for 5's.

Before I get into describing how to use the abacus, there are some fundamentals to know. An abacus is NOT a calculator - it does not give you a mathematical answer. The abacus is a tool to help break down calculations into manageable pieces that are easy to go through. The idea is to make math as simple as needed to require little thinking. It will then keep track of your work.

Usually each string is a different units holder: ones, tens, hundreds, etc. Although you can build an abacus with a different base unit all the time. Each bead represents one (or sometimes 5) or any other number you want. These are what you keep track with.

Now...on to math on the abacus. You can do addition, subtraction, division and multiplication fairly easy on the abacus. With some work you can also do square roots and the like. Basically for addition and subtraction: you set the number you will add to (or take from) on your abacus and begin adding the other number one unit place at a time. The abacus can help you carry digits easily (you can use a concept of the residual number - ie. you are adding 6 to 7, clear the 7 and subtract 4 - the residual or 10 minus 6 - after you add a tens digit).

Example: 135 + 321 = 456
Step 1: With rod H acting as the unit rod, set 135 on rods FGH. (Fig.12)
Step 2: Add 3 to hundreds rod F.Step 3: Add 2 to tens rod G.Step 4 and the answer: Add 1 to units rod H leaving the answer 456 on rods FGH. (Fig.13)

For higher functions (like multiplication and division) you actually set both numbers on the abacus spaced apart.

Now instead of laying out a whole discussion here I point you in two directions. The first is an excellent tutorial on each of the functions. The second is an online abacus you can play with.

• Abacus: Mystery of the Bead
• Online Abacus

The whole concept is actually kind of neat, and once you get into the hang of it, you can move along nicely. Just note - to use it you must now single digit addition, subtraction, division and times tables. Otherwise you won't find it helpful at all.

100 Hour Board