abacus (ăbˈəkəs, əbăkˈ–) [key], in mathematics, simple device for performing arithmetic calculations. The type of abacus now best known is represented by a frame with sliding counters. An elementary abacus might have ten parallel wires strung between two boards on a frame, with nine beads on each wire. Each bead on a given wire has the same value: either ten or some multiple or submultiple of ten. For example, all of the beads on a particular wire may have a value of 1, making this the units wire, or 10, making this wire the tens wire. Numbers are represented and added together on the abacus by grouping beads together. To represent 155, five beads on the units wire are separated from the others on that wire, five beads on the tens wire, and one bead on the hundreds wire. To add 243 to 155, three more beads on the units wire are slid over to join the group of five, four more beads on the tens wire join the five there, and two more beads on the hundreds wire join the one there. The number 398 is now represented on the abacus. Subtraction can be performed by separating groups of beads. More elaborate processes are used to perform multiplication and division. The abacus is used for calculating in the Middle East, Asia, and Russia and for teaching children the elements of arithmetic in many countries. An apparatus of pebbles or other movable counters was known in antiquity to the Egyptians, Greeks, Romans, and Chinese. A special merit of the abacus was that it simplified the addition and subtraction of numbers written in Roman numerals. Another type of abacus includes a board covered with sand or wax to facilitate making and erasing marks.
See J. M. Pullan, The History of the Abacus (1968); P. H. Moon, The Abacus (1971).