Arithmetic

Arithmetic is a branch of mathematics. The term can be used to refer to everything from simple numerical computations to abstract number theory. The two fundamental operations of arithmetic are addition and multiplication. The result of adding two numbers is called the sum of the numbers. The resulr of multiplying two numbers is called product. Substraction is inverse operation, or the undoing, of addition; the result is called the difference. The inverse of undoing, of multiplication is division; the result is called the quotient. Arithmetic of real numbers, that is, rational and irrational number, is based on a number of properties called field properties.

One explanation for the common avoidance of the word arithmetic stems from the fact that, besides learning numbers and how to deal with them, students are often taught about shapes and the skill of measurements, which takes the subject somewhat beyond the purview of arithmetic. However, the common meaning of "Mental Math" is the skill of carrying out basic calculations in one's head without recourse to paper, pencil, or other ancillary devices. The misnaming of the subject is entrenched in mathematics education literature. The titles Children's Mathematics, Children Doing Mathematics and Children's Mathematical Development (the first is so-so, the second is good, the third is excellent) are characteristic in the field, while Children's Arithmetic and Young Children Reinvent Arithmetic(two classics) are not.