Credit: https://www.flickr.com/photos/pschadler/4932737690 Have you always been curious about how to read an abacus? You have probably seen it on TV or in books. You may wonder how this thing works. Unlike in a calculator, abacus has no visible numbers written on it. How do users, or abacists, find the answer by moving the beads up and down? Do answers magically appear on it?

After reading this page, you will learn about the short history of Japanese abacus, its structure, and how to "read" the beads on it. You will realize that it's not magic but rather an incredible tool used in some parts of the world up to this day.

Image Credit: Paul Schadler | Flickr

## The Ancient Calculator

There are many types of abacus. History has shown that the Romans had been using abaci in their mathematical computations centuries ago. Similarly, the Chinese were found to be using this instrument as early as 2nd century BC. It is not known who introduced the abacus. In this page, I will not try to decipher which race had influenced the other one. I will mainly talk about the Japanese abacus, which is the abacus that I have learned to use.

## The Chinese vs. The Japanese Abacus

In the 17th century, the Chinese had introduced the abacus to the Japanese. Known as soroban, the abacus is a rectangular frame with several vertical rods and one horizontal beam. The Chinese abacus has 7 rounded beads in each rod - 2 beads on the upper part, 5 beads on the lower part. However, with the Chinese abacus, it is almost impossible to do "mental" computations (I'll explain it later). To make mental computations easier, the Japanese had slowly developed their own abacus. The 7 beads in each rod had been reduced to 5 beads. The Japanese abacus is now smaller, wider, and lighter than its Chinese counterpart. The beads have sharper edges for easier control. The Japanese abacus is still manufactured to date and is still taught in schools in Japan.

Credit: http://commons.wikimedia.org/wiki/File%3AChinese-abacus.jpg

Photo: Wikimedia

Credit: http://www.flickr.com/photos/nightwing_26/5020357991/

the Japanese abacus is smaller and easier to manipulate
Photo: Harry Li | Flickr

## Parts of the Japanese Abacus

The Japanese abacus is a rectangular frame consisting of vertical rods. The number of rods is not less than nine and is always an odd number (e.g. 11 rods, 13 rods). The abacus has a horizontal bar that separates the beads into upper and lower sections. The upper section has only one bead per rod. The upper beads are known as heavenly beads1. The lower section consists of four beads called the earth beads2. The reckoning bar3 (the horizontal bar) has dots that are equally distributed along its length. The dot is the starting point of the computation. The rod with the dot is called units rod4. The Japanese abacus is smaller than its counterparts; thus, making it easier to handle. You can easily grab the abacus' body with your hand while using the other hand to move the beads up and down.

parts of the Japanese abacus
Photo: Rainy Kua

## Using the Japanese Abacus

### The Beads' Value and The Units Rods

This is the important part so read carefully. Each heavenly bead is equivalent to 5; each earth bead is equivalent to 1. The units rods (the rods with the dots) are the first digits. You can choose any dots to start with. However, the dot near the center is usually used. The rod on the left side of the units rod is the tens digit, the rod on the left side of the tens digit is the hundreds and so on and so forth. The rods on the right side of the units rod are the decimal places.

On the units rods
1 earth bead raised to the reckoning bar means 1.
2 earth beads raised to the reckoning bar means 2.
A heavenly bead lowered to the reckoning bar means 5.
And so on and so forth.

On the tens digit
1 earth bead raised to the reckoning bar means 10.
3 earth beads raised to the reckoning bar means 30.
A heavenly bead lowered to the reckoning bar means 50.
And so on and so forth.

On more than 2 rods
A heavenly bead lowered to the reckoning bar on the third rod to the left,
4 earth beads raised to the reckoning bar on the second rod to the left,
0 earth bead is raised to the reckoning bar on the units rod,
3 earth beads raised to the reckoning bar on the first rod to the right,
A heavenly bead lowered to the reckoning bar on the second rod to the right,
Means you have 540.35!

Credit: http://commons.wikimedia.org/wiki/File:Soroban2.jpg

the Japanese abacus illustrating numbers 1 to 9 from right to left
Photo: Wikimedia Commons

## The Mental Calculation

In abacus classes, once the students had learned the basics of using the abacus, they will be taught to calculate without it! That's right; they will be given long lists of numbers to be added or subtracted, or large digits to be multiplied or divided using only their imaginary abacus. With the present structure of the Japanese abacus, it's "easier" for abacists to visualize the single row of heavenly beads and four rows of earth beads. This is known as anzan in Japanese and xin suan in Chinese. Beginners can learn adding and subtracting mentally. However, multiplying large digits is very difficult for beginners and needs more training. As of this writing, only one person can do mental multiplication of two 7-digit numbers.