**Arithmetic**, usually studied throughout elementary school, deals with subsets of the real number system (whole numbers, integers, and so forth), along with the accompanying operations of arithmetic that may be applied to them. "Higher arithmetic" is sometimes used as another name for number theory.

The number systems studied in arithmetic include:

- Natural numbers and whole numbers (exact definitions vary)
- Integers (including zero and negative numbers)
- Rational numbers (including decimal numbers and fractions)
- Irrational numbers
- Real numbers

The major operations of arithmetic include:

Other important concepts, objects and techniques in arithmetic include:

- Counting
- Number versus numeral
- Percents
- Powers
- Base and exponent
- Roots and radicals
- Scientific notation
- Long division
- Prime numbers and composite numbers
- Divisibility and divisors
- Prime factorization
- Greatest common factor
- Least common multiple
- Order of operations
- Simplifying
- Reducing a fraction
- Least common denominator
- Reducing a radical