While the first documentation of a Chinese Abacus has been dated around the 14th century, some form of the abacus or counting rods have appeared in history as early as 2700 BC in ancient Sumaria. Mentioned in ancient Roman texts, as well as among Egyptian hieroglyphics and Greek artifacts dated as early as 300 BC, the abacus has survived the centuries with its purpose intact. It is basically a tool for counting and performing basic arithmetic. Most often constructed of a wood frame with beads sliding on wire or wooden pegs, the abacus is still used today in many cultures.
An abacus is divided into two parts by a long divider that stretchs horizontally across the frame. Above this divider is "Heaven" where two beads reside on each vertical peg. Each bead in "Heaven" represents a count of five units.Below the divider resides "Earth" where 5 beads reside on each vertical peg. Each bead represents one unit.Division also occurs vertically on the abacus. Each vertical peg represents a numerical sequence of "tenths". For example, reading left to right, the first vertical peg represents one unit, the second ten units, the third one hundred units, the fourth one thousand units and so on.
Using the abacus is simply done by moving the appropriate number of beads down towards the divider or back to the starting point for subtraction. For example:Keeping in mind the above reference, it is easy to process single numbers on the abacus board. The number seven is simply on bead from "heaven" which represents five units and two beads from "earth" which represents one unit each. These beads would be brought to the divider.
Larger numbers are also processed the same way. Again, keeping in mind the values for the beads and the vertical pegs, the number 97 is represented by 1 bead from Heaven and 2 from Earth on the first peg, and 1 bead from Heaven (representing 50) and 4 beads from Earth (representing 40) moved towards the divider but on the second peg.
Adding and subtracting is done much the same way. It is simply a combination of moving beads up or down the pegs on the board. If the first number of the equation is smaller than 5, but will become greater than 5 after the addition, one bead from Heaven is moved towards the divider (representing 5 units) on the first vertical peg and one or more beads from Earth are put back into place. When the equation becomes greater than 10 on the first peg, beads are moved from either or both Heaven and Earth and 1 bead is added to the vertical peg directly to the right.
For example: To add the numbers 7 + 5, you would first place the first number (7) on the abacus board on the first peg. Then, since the number will total greater than 10 upon completion, the 1 bead from Heaven on the first peg (shown in red in the picture above) is put back into place, and 1 bead from Earth on the second vertical peg is brought to the center (shown in green on the picture). This then becomes the representation for 12.
Practicing with the abacus board is the best way to become familiar with how to work it. Start with simple equations, and proceed to ever more difficult ones.