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In arithmetic and higher mathematics, subtraction is the inverse operation of addition.

In lower-level elementary mathematics and when using signed integers in programming languages, subtracting a number from a number where the result is outside the range is undefined.

Subtraction in different fields

  • Integer subtraction: a - b is equivalent to a + -b, where -b is the additive inverse of b.
    • Example: 9 - 8 = 1
  • Real number and complex number subtraction:
    • Example: 8.2 - (5 + 2i) = 3.2 - 2i
  • Matrix subtraction: A - B = A + -B, A+B×-1, A+B÷-1

Properties

  • Generally, subtraction is not commutative nor associative.
  • 3 - 6 ≠  6 - 3
  • But keep in mind that 6-3=3 and 3-6=negative3, so switching the subtrahend with the minuend gives the inverse difference.

In real life.

Subtraction is used in real life like addition like in computing change, calculating the amount remaining from a bank account, and many others.

Estimation

This can be done in the same way as addition.

Table of basic subtractions

See also

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