Subtraction - The Definitions Of Subtraction, Terminology, Properties, Uses Of Subtraction
addition inverse
Subtraction is the operation that is the inverse of addition. Subtracting a number has the effect of nullifying the addition of that same number. For example, if one adds 11 to 41 then subtracts 11, the result is 41 again.
Symbolically, for any numbers a and b, (a + b) - b = a
Or one can subtract first, then add: (a - b) + b = a
Thus, one can say that subtraction and addition are "inverse operations."
Additional Topics
The second of the two rules above can be taken as a definition of subtraction. That is "the difference of two numbers, a - b, is the number which must be added to the second number, b, to equal the first, a." Before the widespread use of electronic cash registers, grocery clerks and others, making change, would use this definition directly. If, for example, a customer bought grocerie…
It matters very much which of the two parts of a difference are named first. Taking $500 from an account with $300 in it is very different from taking $300 from $500. For this reason, subtraction is not commutative: a - b does not equal b - a. Subtraction is not associative either: (a - b) - c does not equal a - (b - c). An example will demonstrate this: (20 - 10) - 3 is 7, but 20 - (10 - 3) is 13…
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