Arithmetic

The arithmetic value of a number is the number stripped of any negative sign. For number x it is expressed as |x|, termed the modulus of x; compare algebraic. The arithmetic mean of n numbers is their collective algebraic sum.Applied to a series of numbers, ‘arithmetic’ indicates that adjacent members differ by a constant additive increment, the ‘common difference’ (any finite number). for some value a. Compare geometric.

For measurement scales, ‘arithmetic’ means that a step of any one size in the scale value represents the same amount of additive change in the measured item, regardless of place on the scale. The traditional British and US scales for shoe size, where 1 equates to a third of an inch, is arithmetic.
(It should be noted that a simple arithmetic increase in a diameter has a squared effect on circular cross-section and spherical surface area, a cubed effect on volume and hence mass, etc.)

The mathematics of integers, rational numbers, real numbers, or complex numbers under addition, subtraction, multiplication, and division.
[Middle English arsmetike, from Old French arismetique, from Medieval Latin arismetica, alteration of Latin arithmētica, from Greek arithmētikē (tekhnē), (art) of counting, feminine of arithmētikos, from arithmein, to count, from arithmos, number.]

Arithmetic or arithmetics (from the Greek word ἀριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers. Professional mathematicians sometimes use the term (higher) arithmetic when referring to more advanced results related to number theory, but this should not be confused with elementary arithmetic.