Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. Besides counting fruits, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more.

Addition follows several important patterns. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. All of these rules can be proven, starting with the addition of natural numbers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.

Performing addition is one of the simplest numerical tasks. 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 animals. 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.

### Other articles related to "addition":

Semiring
... A semiring is a set R equipped with two binary operations + and ·, called addition and multiplication, such that (R, +) is a commutative monoid with identity element 0 (a + b ... The difference between rings and semirings, then, is that addition yields only a commutative monoid, not necessarily a commutative group ... in semirings do not necessarily have an inverse for the addition ...
... In chapter 9 of Lewis Carroll's Through the Looking-Glass, the White Queen asks Alice, "And you do Addition?.. ... and the Red Queen declares, "She can't do Addition" ...
Westview High School (San Diego) - Academics
... In addition to the four daily classes, there are various other periods such as Homeroom, Silent Sustained Reading (SSR), and Wolverine Time, a tutorial period, which occur only on specific days of the week ... In addition to the required ninth-grade physical education requirement, one other physical education course is needed ... In addition to one Honors course, all Advanced Placement courses are assigned values of 5, 4, 3, and 0, for these grades ...
Japanese Aircraft Carrier Ryūjō - Design - Hull
... This necessitated the addition of a second hangar atop the first, raising freeboard to 15 m (49 ft) ... Even the addition of Sperry active stabilizers failed to compensate for the inherent instability of the new design and in 1934 Ryūjō was taken in hand for extensive ... Changes included strengthening of the keel, the addition of enlarged bulges to either side of the hull and the removal of two twin 127mm AA gun mountings to reduce her top weight ...
Elementary Arithmetic - Addition - Example
... Say one wants to find the sum of the numbers 653 and 274 ... Write the second number under the first one, with digits aligned in columns, like so 4 ... Then draw a line under the second number and put a plus sign ...

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