Many people think of arithmetic and mathematics as the same thing. Arithmetic, however, is defined as the most basic and fundamental category of mathematics. It includes computations that involve adding, subtracting, dividing, and multiplying numbers that are real, rational, and complex. This differs from mathematics, which involves studying number, shape, and quantity relationships. Mathematics also includes the use of not only signs and symbols, but also proofs.

When a person studies arithmetic, he learns how to work with numbers and do basic calculations. For example, he learns how to recognize and name quantities as well as how to add numbers together and subtract them. He also learns how to multiply numbers and divide them. This basic study typically provides a foundation students can use for calculation in everyday life as well as in preparation for more complicated work with numbers, such as in algebra and calculus.

Though arithmetic is considered a basic form of math, it is widely used. Typically, people use it in the course of everyday life. For example, they use it when counting, making purchases, preparing budgets, and balancing their checkbooks. It is also used by businesses that have to make accounting calculations. It often has a place in some higher-level scientific calculations as well.

Addition is one of the basic types of arithmetic. It essentially involves combining numbers, which are referred to as addends, to get a total, which is called the sum. Subtraction is another basic operation of this type of math. It is the opposite of addition and involves finding the difference between numbers. The original number in a subtraction problem is called the minuend while the number that is subtracted is called the subtrahend.

Multiplication is another arithmetic operation; it involves adding numbers in a quick way. For example, a multiplication problem that involves multiplying two times four is basically adding two plus two plus two plus two—quickly. The numbers that are multiplied in this type of problem are called factors, and the answer is called the product. Division is the opposite of multiplication and involves splitting a number or quantity into equal parts. The original number is called the dividend, the number a person divides by is called the divisor, and the answer to a division problem is called the quotient.

Sometimes the word arithmetic is used to mean number theory. This, however, differs from the form of elementary math most people mean when they talk about arithmetic. Number theory involves the study of the properties of numbers.