# associative law

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## associative law,

in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9. More generally, in addition, for any three numbers a, b, and c the associative law is expressed as (a+b)+c=a+(b+c). Multiplication of numbers is also associative, i.e., (a×bc=a×(b×c). In general, any binary operation, symbolized by +, joining mathematical entities A, B, and C obeys the associative law if (A+B)+C=A+(B+C) for all possible choices of A, B, and C. Not all operations are associative. For example, ordinary division is not, since (60÷12)÷3=5÷3=5/3, while 60÷(12÷3)=60÷4=15. When an operation is associative, the parentheses indicating which quantities are first to be combined may be omitted, e.g., (2+3)+4=2+(3+4)=2+3+4.

## associative law

[ə′sō·sē‚ād·iv ′lȯ]
(mathematics)
For a binary operation that is designated °, the relationship expressed by a ° (b ° c)=(a ° b) ° c.
References in periodicals archive ?
When teachers analysed this student's thinking they realised that this student had used an understanding of equivalence and the associative law, possibly unconsciously, to find the left-hand side sum.
It exploits the fact that, under these circumstances, the usual properties of multiplication no longer apply (associative law and distributive law as compared to addition).
Since [[??].sub.1] [subset] [??] and O([[??].sub.1]) [subset] O([??]), the associative law and distribute law are also true for the [[??].sub.1].
Generalized commutative laws and generalized associative laws of interval-valued fuzzy soft sets are obtained as well.
Next, we investigate properties of soft product operations by considering associative laws.

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