Subtractions

Subtraction is a basic arithmetic operation that computes the difference between two numbers. It is denoted by the minus sign and written as a − b, where a is the minuend (the quantity from which another quantity is subtracted) and b is the subtrahend (the quantity to be subtracted). The result is called the difference.

Subtraction is the inverse operation of addition in the sense that a − b = a + (−b). This relationship underpins many algebraic rules and problem-solving techniques. In many contexts subtraction is defined for numbers in a field, such as integers, rationals, reals, and complex numbers, and can be extended to vectors or matrices by performing componentwise subtraction.

In the natural numbers, subtraction may yield a nonnegative result only if a ≥ b; otherwise the result is negative, which requires expanding the number system or using signed numbers. Practical computation often uses column subtraction with borrowing, and decimal alignment is essential when working with fractional parts. In computer arithmetic, subtraction is implemented at hardware or software levels, typically using representations such as two’s complement for signed integers.

Historical notes include the long-standing use of subtraction across many cultures, and the development of symbolic notation. The terms minuend and subtrahend come from Latin, meaning roughly “the thing to be diminished” and “the thing to be subtracted,” respectively. The minus sign itself was adopted in medieval Europe and later standardized in mathematical notation.

Subtraction plays a central role in measurement, accounting, and problem solving, and serves as the foundation for more advanced operations, including solving equations and analyzing differences between quantities.