Plus and Minus Signs - Minus Sign

Minus Sign

The minus sign has three main uses in mathematics:

1. The subtraction operator: A binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
2. Directly in front of a number and when it is not a subtraction operator it means a negative number. For instance −5 is negative 5.
3. A unary operator that acts as an instruction to replace the operand by its opposite. For example, if x is 3, then −x is −3, but if x is −3, then −x is 3. Similarly, −(−2) is equal to 2.

All three uses can be referred to as "minus" in everyday speech. In modern US usage, −5 (for example) is normally pronounced "negative five" rather than "minus five". "Minus" may be used by speakers born before 1950, and is still popular in some contexts, but "negative" is usually taught as the only correct reading. In most other parts of the English-speaking world, "minus five" is more common. Textbooks in America encourage −x to be read as "the opposite of x" or even "the additive inverse of x" to avoid giving the impression that −x is necessarily negative.

In some contexts, different glyphs are used for these meanings; for instance in the computer language APL a raised minus sign is used in negative numbers (as in 2 − 5 gives −3), but such usage is rare.

In mathematics and most programming languages, the rules for the order of operations mean that −52 is equal to −25. Powers bind more strongly than multiplication or division which binds more strongly than addition or subtraction. While strictly speaking, the unary minus is not subtraction, it is given the same place as subtraction. However in some programming languages and Excel in particular, unary operators bind strongest, so in these −5^2 is 25 but 0−5^2 is −25.