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Addition is associative: when adding three or more numbers, the order of operations does not matter.

When addition is used together with other operations, the order of operations becomes important.

In the standard order of operations, addition is a lower priority than exponentiation, nth roots, multiplication and division, but is given equal priority to subtraction.

Even some nonhuman animals show a limited ability to add, particularly primates.

In a 1995 experiment imitating Wynn's 1992 result (but using eggplants instead of dolls), rhesus macaque and cottontop tamarin monkeys performed similarly to human infants.

However, if a measure of 5 feet is extended by 2 inches, the sum is 62 inches, since 60 inches is synonymous with 5 feet.

On the other hand, it is usually meaningless to try to add 3 meters and 4 square meters, since those units are incomparable; this sort of consideration is fundamental in dimensional analysis.

Besides counting fruits, addition can also represent combining other physical objects.

Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices. It is commutative, meaning that order 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 (see Summation).

Studies on mathematical development starting around the 1980s have exploited the phenomenon of habituation: infants look longer at situations that are unexpected.

Another 1992 experiment with older toddlers, between 18 and 35 months, exploited their development of motor control by allowing them to retrieve ping-pong balls from a box; the youngest responded well for small numbers, while older subjects were able to compute sums up to 5.

The sum a b can be interpreted as a binary operation that combines a and b, in an algebraic sense, or it can be interpreted as the addition of b more units to a.