subtracted

Subtracted is the past participle of subtract. In mathematics, subtraction is a binary operation that takes two numbers, usually called the minuend and the subtrahend, and yields their difference. The act of subtracting the subtrahend from the minuend decreases the first quantity by the second, and the result is called the difference. For example, 7 − 3 = 4; the difference is 4. Subtraction is the inverse operation of addition because a − b equals a plus the additive inverse of b, namely a + (−b).

Properties: Order matters: a − b generally differs from b − a; subtraction is not commutative. It is also not associative; (a − b) − c does not equal a − (b − c) in general. In many contexts subtraction is defined through addition: a − b = a + (−b).

Extensions and uses: Subtraction applies to integers, rational numbers, and real numbers; in higher-dimensional contexts, subtraction is extended component-wise for vectors and matrices, provided the underlying structure supports an additive inverse. In practical terms, subtracting is used to remove quantities, compute differences, compare values, and adjust totals in finance, measurement, and inventory.

Subtracted as a term also appears in everyday language to indicate removal of items or quantities, as in “the subtracted tax” or “the amount subtracted from the total.” Subtraction has origins in ancient arithmetic and was formalized in the development of numeral systems and algebra.