"Add" redirects here. For other uses, see ADD (disambiguation).
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.[2] The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples each, totaling at five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides 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. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Addition has several important properties. 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. Repeated addition of 1 is the same as counting (see Successor function). Addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.
Performing addition is one of the simplest numerical tasks to do. 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. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.
Arithmetic operations
v
t
e
Addition (+)
Subtraction (−)
Multiplication (×)
Division (÷)
Exponentiation (^)
nth root (√)
Logarithm (log)
v
t
e
^From Enderton (p. 138): "...select two sets K and L with card K = 2 and card L = 3. Sets of fingers are handy; sets of apples are preferred by textbooks."
^Lewis, Rhys (1974). "Arithmetic". First-Year Technician Mathematics. Palgrave, London: The MacMillan Press Ltd. p. 1. doi:10.1007/978-1-349-02405-6_1. ISBN 978-1-349-02405-6.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication...
polar addition reactions: electrophilic addition and nucleophilic addition. Two non-polar addition reactions exist as well, called free-radical addition and...
The additions of Daniel are three chapters not found in the Hebrew/Aramaic text of Daniel. The text of these chapters is found in the Koine Greek Septuagint...
chemistry, an addition polymer is a polymer that forms by simple linking of monomers without the co-generation of other products. Addition polymerization...
Oxidative addition and reductive elimination are two important and related classes of reactions in organometallic chemistry. Oxidative addition is a process...
In organic chemistry, syn- and anti-addition are different ways in which substituent molecules can be added to an alkene (R2C=CR2) or alkyne (RC≡CR). The...
In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its...
multiplication on F 2 {\displaystyle \mathbb {F} _{2}} and the "XOR" operation as addition on F 2 {\displaystyle \mathbb {F} _{2}} : r = p ∧ q ⇔ r = p ⋅ q ( mod 2...
In mathematics, an addition theorem is a formula such as that for the exponential function: ex + y = ex · ey, that expresses, for a particular function...
In organic chemistry, an electrophilic addition (AE) reaction is an addition reaction where a chemical compound containing a double or triple bond has...
is not an inverse of the sum operation. Instead it replaces the vector addition of the Minkowski sum with a vector subtraction. If the two convex shapes...
In organic chemistry, the Michael reaction or Michael 1,4 addition is a reaction between a Michael donor (an enolate or other nucleophile) and a Michael...
Simple Addition or Totals is a family of patience or card solitaire games that share certain aims and procedures. Moyse counts the games of Elevens, Fifteens...
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector, v → {\displaystyle...
In four-color printing (or more), under color addition (UCA) is a technique for darkening areas of the printed image by adding colored inks. It is meant...
Addition Elle was a Canadian clothing store chain that sold plus-size clothing. It was established in Montreal and sold to Reitmans in 2001. It closed...
prescription at the top of the lens and reaches a maximum addition power, or the full reading addition, at the bottom of the lens. The length of the progressive...
The Standard addition method, often used in analytical chemistry, quantifies the analyte present in an unknown. This method is useful for analyzing complex...
In organic chemistry, a nucleophilic addition (AN) reaction is an addition reaction where a chemical compound with an electrophilic double or triple bond...
Addition and subtraction may refer to: Addition Subtraction Addition and Subtraction is a 1900 French film. This disambiguation page lists articles associated...
Modular additions are usually side and second-story additions to homes that are pre-fabricated at the facilities. General characteristics of a modular...
The mere addition paradox (also known as the repugnant conclusion) is a problem in ethics identified by Derek Parfit and discussed in his book Reasons...
Operation Addition was the name given to the Canadian contribution to United Nations Mission in Ethiopia and Eritrea, the United Nations peacekeeping forces...
In combinatorics, the addition principle or rule of sum is a basic counting principle. Stated simply, it is the intuitive idea that if we have A number...
Parallel addition may refer to: Parallel (operator), a mathematical operation used in electrical engineering Parallel addition (computing), a digital...
The Kharasch addition is an organic reaction and a metal-catalysed free radical addition of CXCl3 compounds (X = Cl, Br, H) to alkenes. The reaction is...
In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers starting with 1 and ending with n, such...