"The addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic..."
The process of combining two or more numbers to obtain a sum.
Basic addition: The simple act of combining two or more numbers to find the sum.
Number bonds: Understanding the relationship between numbers that add up to a specific value.
Commutative property: Knowing that changing the order of the numbers being added will not change the final result.
Associative property: Knowing that changing the grouping of the numbers being added will not change the final result.
Identity property: Understanding that adding zero to any number will not change the number.
Sum: Understanding the term used to represent the result of an addition operation.
Addends: Understanding the individual numbers being added.
Regrouping: Knowing how to carry over numbers when adding multi-digit numbers.
Mental math strategies: Learning addition shortcuts, such as counting on, breaking numbers into smaller parts, and using double facts.
Estimation: Understanding how to approximate the sum of two or more numbers without calculating them exactly.
Addition of whole numbers: This is the basic type of addition, consisting of adding two or more integers together.
Addition of decimals: This involves adding two or more decimals together, i.e., numbers with a decimal point.
Addition of fractions: This involves adding two or more fractions with the same denominator, or converting them to a common denominator first.
Addition of mixed numbers: This involves adding a whole number and a fraction, or two mixed numbers, where the fractional part of each number is added separately.
Addition of negative numbers: This involves adding a positive number and a negative number, or two negative numbers, where the signs indicate whether to add or subtract.
Addition of complex numbers: This involves adding two or more numbers in the form of a + bi, where a and b are real numbers, and i is the imaginary unit.
Addition of matrices: This involves adding two or more matrices together, where the corresponding elements in each matrix are added.
Addition of vectors: This involves adding two or more vectors together, where the corresponding components in each vector are added.
Addition of polynomials: This involves adding two or more polynomials together, where the coefficients of each term are added.
"The addition of two whole numbers results in the total amount or sum of those values combined."
"...addition can also be performed on abstract objects such as vectors, matrices, subspaces, and subgroups."
"Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed..."
"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."
"The most basic task, 1 + 1, can be performed by infants as young as five months, and even some members of other animal species."
"Mechanical aids range from the ancient abacus to the modern computer..."
"In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems."
"...where research on the most efficient implementations of addition continues to this day."
"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')."
"...using abstractions called numbers instead, such as integers, real numbers, and complex numbers."
"No, addition can also be performed on abstract objects such as vectors, matrices, subspaces, and subgroups."
"Addition of very small numbers is accessible to toddlers..."
"Performing addition is one of the simplest numerical tasks to do."
"...addition can also be defined and executed without referring to concrete objects..."
"The addition of two whole numbers results in the total amount or sum of those values combined."