| Share
 

associative law

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 ( AB )∘ C = A ∘( BC ) 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.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

More on associative law from Infoplease:

  • associative: meaning and definitions - associative: Definition and Pronunciation
  • ring, mathematical system - ring ring, in mathematics, system consisting of a set R of elements and two binary operations, such ...
  • addition - addition addition, fundamental operation of arithmetic, denoted by +. In counting, a+b represents ...
  • René Waldeck-Rousseau - Waldeck-Rousseau, René Waldeck-Rousseau, René , 1846–1904, French statesman. ...
  • Emmy Noether - Noether, Emmy Noether, Emmy (Amalie Emmy Noether), 1882–1935, German mathematician, b. ...

See more Encyclopedia articles on: Mathematics

24 X 7

Private Tutor

Click Here for Details
24 x 7 Tutor Availability
Unlimited Online Tutoring
1-on-1 Tutoring