# associative law

Also found in: Dictionary.

## 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*×

*b*)×

*c*=

*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.

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## 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*.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page: