Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. Most people learn elementary arithmetic in elementary school.
Elementary arithmetic starts with the natural numbers and the Arabic numerals used to represent them. It requires the memorization of addition tables and multiplication tables for adding and multiplying pairs of digits. Knowing these tables, a person can perform certain well-known procedures for adding and multiplying natural numbers. Other algorithms are used for subtraction and division. Mental arithmetic is elementary arithmetic performed in the head, for example to know that 100 − 37 = 63 without use of paper. It is an everyday skill. Extended forms of mental calculation may involve calculating extremely large numbers, but this is a skill not usually taught at the elementary level.
Elementary arithmetic then moves on to fractions, decimals, and negative numbers, which can be represented on a number line.
Nowadays people routinely use electronic calculators, cash registers, and computers to perform their elementary arithmetic for them. Earlier calculating tools included slide rules (for multiplication, division, logs and trig), tables of logarithms, nomographs, and mechanical calculators.
The question of whether or not calculators should be used, and whether traditional mathematics manual computation methods should still be taught in elementary school has provoked heated controversy as many standards-based mathematics texts deliberately omit some or most standard computation methods. The 1989 NCTM standards led to curricula which de-emphasized or omitted much of what was considered to be elementary arithmetic in elementary school, and replaced it with emphasis on topics traditionally studied in college such as algebra, statistics and problem solving.
In ancient times, the abacus was used to perform elementary arithmetic, and still is in many parts of Asia. A skilled user can be as fast with an abacus as with a calculator, which may require batteries.
In the 14th century Arabic numerals were introduced to Europe by Leonardo Pisano. These numerals were more efficient for performing calculations than Roman numerals, because of the positional system.