Subtraction

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In mathematics, subtraction is one of the four basic arithmetic operations. It is usually denoted by an infix minus sign.

The traditional names for the terms of the subtraction in the formula

c − b = a

are minuend (c) − subtrahend (b) = difference (a).

Subtraction is used to model the following three physical processes. First, from a given collection, take away (subtract) a given number of objects. Second, combine a given measurement with an opposite measurement. For example, combine a movement right followed by a movement left, or combine a deposit and a withdrawal. Third, compare two objects to find their difference. For example, to find the difference between $800 and $600, subtract $800 − $600 = $200.

Mathematically, it is often useful to view subtraction as a kind of addition, addition of the opposite. Thus, we can view 7 − 3 = 4 as the sum of seven and negative three. This allows and requires us to apply to subtraction all of the familiar rules and nomenclature of addition. Subtraction is not commutative (in fact, it is anticommutative) or associative, but addition of signed numbers is. Professional mathematicians seldom used the words minuend and subtrahend but rather consider 7 − 3 = 4 to be the sum of two terms, seven and negative three.