How Does a Chinese Abacus Work?

Board Setup

The ancient abacus usually consisted of a wooden structure. Four flat sides form a rectangle. Running vertically along the rectangle are thin cylindrical pieces of wood attached to the two width-ends. Sitting close to two-thirds of the way up, one more horizontal divider exists, separating the abacus into two distinct sections. Around each cylindrical column sits several flattened, round button-like beads, each containing a hole in the center to allow them free movement up and down the column.

The abacus comes in several types; however, most of the ancient versions contain 13 rows divided into two sections within each row. These versions contain two beads on the smaller, top-part of the abacus, and five beads on the lower, larger area. A few modern versions contain one bead on the top row with five on the bottom, and others consist of one bead on top and four on bottom. The starting position of the top beads is always toward the top wall of the abacus, while the lower beads will always be pushed towards the lower wall as a starting position.

Number representation is fairly easy to grasp on an abacus. Each row can be thought of as a “ten’s place,” much like written numbers. From right to left, row number one represents the “one’s column” and the second column represents the “ten’s place.” The third column represents the “hundred’s place,” and so on from there. Each button in the top and smaller section of the abacus represents the value of five in its respective column, while each bead in the lower column represents the value of one. Representing the number “135” consists of moving one bead from the third row in the large section, three bead from the second row in the large section, and one bead from the first row in the small section.

Although it takes practice, performing arithmetic operations can be achieved in a relatively short amount of time. The first step to performing an operation is finding the number on the board. Once a number is set, you add or subtract each column as necessary based on the new number at hand. For example, seven (which consists of one top and two lower beads from the first row) added to two (which consists of two lower beads in the first row) means shifting seven beads on top of your current number (two in this case). To do this, you will add the additional two lower beads and one top bead onto the current two already in place. The resulting value after the calculation is the answer.