Subtraction

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

$-$	$-\frac{1}{0}$	$-1$	$-0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$-\frac{1}{0}$	$\frac{0}{0}$	$\frac{1}{0}$	$\frac{1}{0}$	$\frac{0}{0}$	$\frac{1}{0}$	$\frac{1}{0}$	$\frac{0}{0}$
$-1$	$-\frac{1}{0}$	$0$	$1$	$\frac{0}{0}$	$1$	$2$	$\frac{1}{0}$
$-0$	$-\frac{1}{0}$	$-1$	$0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$
$0$	$-\frac{1}{0}$	$-1$	$-0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$1$	$-\frac{1}{0}$	$-2$	$-1$	$\frac{0}{0}$	$-1$	$0$	$\frac{1}{0}$
$\frac{1}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$\frac{0}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$\frac{0}{0}$

See also

• Addition
• Subtrahend
• Minuend
• Difference