page_title: Subtraction
section_title: Notation and terminology
hierarchical_section_title: Subtraction / Notation and terminology
caption_attribution_description: English: Subtraction of numbers 0-10. Line labels = first number. X axis = second number. Y axis = difference.
context_page_description: Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign, −. For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, resulting in a total of 3 apples. Therefore, the difference of 5 and 2 is 3, that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.
  Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is also not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because 0 is the additive identity, subtraction of it does not change a number. Subtraction also obeys predictable rules concerning related operations, such as addition and multiplication.
context_section_description: Subtraction is usually written using the minus sign "−" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,
   (pronounced as "two minus one equals one")
   (pronounced as "four minus two equals two")
   (pronounced as "six minus three equals three")
   (pronounced as "four minus six equals negative two")
  There are also situations where subtraction is "understood", even though no symbol appears:
  A column of two numbers, with the lower number in red, usually indicates that the lower number in the column is to be subtracted, with the difference written below, under a line. This is most common in accounting.
  Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.
  All of this terminology derives from Latin. "Subtraction" is an English word derived from the Latin verb subtrahere, which in turn is a compound of sub "from under" and trahere "to pull". Thus, to subtract is to draw from below, or to take away. Using the gerundive suffix -nd results in "subtrahend", "thing to be subtracted". Likewise, from minuere "to reduce or diminish", one gets "minuend", which means "thing to be diminished".
caption: Subtraction of numbers 0–10. Line labels = minuend. X axis = subtrahend. Y axis = difference.
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