The plus sign "+" ( Unicode:U+002B ASCII: +) is an abbreviation of the Latin word et, meaning "and". The later Middle English terms "adden" and "adding" were popularized by Chaucer. Addere and summare date back at least to Boethius, if not to earlier Roman writers such as Vitruvius and Frontinus Boethius also used several other terms for the addition operation. This is appropriate not only because the sum of two positive numbers is greater than either, but because it was common for the ancient Greeks and Romans to add upward, contrary to the modern practice of adding downward, so that a sum was literally higher than the addends. "Sum" and "summand" derive from the Latin noun summa "the highest, the top" and associated verb summare. Redrawn illustration from The Art of Nombryng, one of the first English arithmetic texts, in the 15th century. Likewise from augere "to increase", one gets "augend", "thing to be increased". Using the gerundive suffix -nd results in "addend", "thing to be added". " Addition" and " add" are English words derived from the Latin verb addere, which is in turn a compound of ad "to" and dare "to give", from the Proto-Indo-European root *deh₃- "to give" thus to add is to give to. Īll of the above terminology derives from Latin. Today, due to the commutative property of addition, "augend" is rarely used, and both terms are generally called addends. In fact, during the Renaissance, many authors did not consider the first addend an "addend" at all. Some authors call the first addend the augend. This is to be distinguished from factors, which are multiplied. This terminology carries over to the summation of multiple terms. The numbers or the objects to be added in general addition are collectively referred to as the terms, the addends or the summands Term + term summand + summand addend + addend augend + addend } = Terms Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Addition of very small numbers is accessible to toddlers the most basic task, 1 + 1, can be performed by infants as young as five months, and even some members of other animal species. Performing addition is one of the simplest numerical tasks to do. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. Repeated addition of 1 is the same as counting (see Successor function). It is commutative, meaning that the order of the operands does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.Īddition has several important properties. Addition belongs to arithmetic, a branch of mathematics. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").īesides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. The example in the adjacent image shows two columns of three apples and two apples each, totaling at five apples. The addition of two whole numbers results in the total amount or sum of those values combined. For other uses, see ADD (disambiguation).ģ + 2 = 5 with apples, a popular choice in textbooks Īddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.
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