#2 + a + b = a + 2 + b# is an example of which algebraic property?

1 Answer
George C.
Oct 25, 2015

It is an example of at least two algebraic properties:

Commutativity and associativity.

Explanation:

Addition is:

Commutative: #A+B = B+A#

Associative: #(A+B)+C = A+(B+C)#

The example #2+a+b = a+2+b# uses commutativity to get #2+a = a + 2# and hence #2+a+b = a+2+b#.

The example also uses associativity to even write #2 + a + b#. Without associativity, we would need to write: #(2+a)+b# or #2+(a+b)#, etc.

The example also expresses equality, which might also be counted as an algebraic property, but is often just assumed.

Related questions
See all questions in Properties of Rational Numbers
Impact of this question
7737 views around the world
You can reuse this answer
Creative Commons License