Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools.

In numeral systems, digits are characters used to represent the value of numbers. An example of a numeral system is the predominantly used Indo-Arabic numeral system (0 to 9), which uses a decimal positional notation. Other numeral systems include the Kaktovik system (often used in the Eskimo-Aleut languages of Alaska, Canada, and Greenland), and is a vigesimal positional notation system. Regardless of the numeral system used, the results of arithmetic operations are unaffected.

In elementary arithmetic, the successor of a natural number (including zero) is the next natural number and is the result of adding one to that number. The predecessor of a natural number (excluding zero) is the previous natural number and is the result of subtracting one from that number. For example, the successor of zero is one, and the predecessor of eleven is ten (${\displaystyle 0+1=1}$ and ${\displaystyle 11-1=10}$). Every natural number has a successor, and every natural number except 0 has a predecessor.

The natural numbers have a total ordering. If one number is greater than (${\displaystyle >}$) another number, then the latter is less than (${\displaystyle <}$) the former. For example, three is less than eight (${\displaystyle 3<8}$), thus eight is greater than three (${\displaystyle 8>3}$). The natural numbers are also well-ordered, meaning that any subset of the natural numbers has a least element.

Counting assigns a natural number to each object in a set, starting with 1 for the first object and increasing by 1 for each subsequent object. The number of objects in the set is the count. This is also known as the cardinality of the set.

Counting can also be the process of tallying, the process of drawing a mark for each object in a set.

Addition is a mathematical operation that combines two or more numbers (called addends or summands) to produce a combined number (called the sum). The addition of two numbers is expressed with the plus sign (${\displaystyle +}$). It is performed according to these rules:

When the sum of a pair of digits results in a two-digit number, the "tens" digit is referred to as the "carry digit". In elementary arithmetic, students typically learn to add whole numbers and may also learn about topics such as negative numbers and fractions.