Multiplication

Along with addition, subtraction, and division, multiplication is one of the four fundamental arithmetic operations

Mathematics has enormously broadened its horizons in the last centuries, and multiplication has followed its path, finding application in gradually different fields. Multiplication is possible between integers, fractions, real numbers, complex numbers, polynomials, sets, vectors, matrices, and more. But the most elementary and ancient form of multiplication is and remains that between natural numbers.

Multiplication as a recursive addition

This fundamental type of multiplication is based upon the idea of ​​a recursive addition, i.e., an addition repeated as many times as required by the factor by which a number is multiplied. For instance, what does it mean to multiply 4×6? It means repeating the addition 4+4 six times in a row. Thus, multiplication is essentially a shortcut to make the addition operation more concise:

The more numerous the addends are, the greater the advantage of this compact form of writing: