An abacus represents place values in different columns. Moving its beads records numbers and carrying, allowing addition, subtraction, multiplication, and division to be broken into sequences of operations.
Chinese abacuses differ from counting boards and abacuses found elsewhere. They are both practical tools and educational aids for developing calculation skills.
China
The Chinese abacus, also known as the suanpan, comes in various lengths and widths, depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom one, to represent numbers in a bi-quinary coded decimal-like system. The beads are usually rounded and made of hardwood. The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not. One of the top beads is 5, while one of the bottom beads is 1. Each rod has a number under it, showing the place value. The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.
The prototype of the Chinese abacus appeared during the Han dynasty, and the beads are oval. The Song dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus including the shape of the beads commonly known as Japanese-style abacus.
In the early Ming dynasty, the abacus began to appear in a 1:5 ratio. The upper deck had one bead and the bottom had five beads. In the late Ming dynasty, the abacus styles appeared in a 2:5 ratio. The upper deck had two beads, and the bottom had five.
Various calculation techniques were devised for suanpan enabling efficient calculations. Some schools teach students how to use it.
In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).
The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, given evidence of a trade relationship between the Roman Empire and China. However, no direct connection has been demonstrated, and the similarity of the abacuses may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. Incidentally, this ancient Chinese calculation system (Shì yòng zhì) allows use with a hexadecimal numeral system (or any base up to 18) which is used for traditional Chinese measures of weight. Instead of running on wires as in the Chinese, Korean, and Japanese models, the Roman model used grooves, presumably making arithmetic calculations much slower.
Mesopotamia
The Sumerian abacus appeared between 2700 and 2300 BC. It held a table of successive columns which delimited the successive orders of magnitude of their sexagesimal (base 60) number system. Primitive forms of the abacus existed in Sumer, such as the non-fixed bead abacus, a line of strings fixed to a board, counting strings consisting of beads (similar to prayer beads and pace count beads), ropes and knots, and counting boards (similar to tally sticks). The exact form and function of these devices are scattered around different sources, and their exact relation to the modern abacus is unknown but it is almost certain there is a relationship with masihatu, which functioned similar to an abacus utilizing multiple strings and sets of beads.
Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "seem to have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".