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Subtraction is a mathematical operation that represents the operation of removing objects from a collection. It is signified by the minus sign (−). For example, in the picture on the right, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, 5 − 2 = 3. Besides counting fruits, subtraction can also represent combining other 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 not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Subtraction of 0 does not change a number. Subtraction also obeys predictable rules concerning related operations such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra. Performing subtraction is one of the simplest numerical tasks. Subtraction of very small numbers is accessible to young children. In primary education, students are taught to subtract numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. ==Notation and terminology== Subtraction is written using the minus sign "−" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example, : (verbally, "two minus one equals one") : (verbally, "four minus two equals two") : (verbally, "six minus three equals three") : (verbally, "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 is in turn a compound of ''sub'' "from under" and ''trahere'' "to pull"; thus to ''subtract'' is to ''draw from below, take away''. Using the gerundive suffix ''-nd'' results in "subtrahend", "thing to be subtracted".〔"Subtrahend" is not a Latin word; in Latin it must be further conjugated, as in ''numerus subtrahendus'' "the number to be subtracted".〕 Likewise from ''minuere'' "to reduce or diminish", one gets "minuend", "thing to be diminished". 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「subtraction」の詳細全文を読む スポンサード リンク
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