Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
The associative property of addition states that the way in which numbers are grouped when adding does not change their sum. Mathematically, this is expressed as $(a + b) + c = a + (b + c)$.
5 Must Know Facts For Your Next Test
The associative property of addition applies to real numbers.
Grouping symbols like parentheses can be rearranged without changing the sum.
The property is crucial for simplifying algebraic expressions.
It ensures consistency in calculations regardless of how terms are grouped.
A mathematical principle stating that the order in which two numbers are added or multiplied does not affect their sum or product, respectively: $a + b = b + a$ and $a \times b = b \times a$.
A property indicating that multiplying a number by a group of numbers added together is the same as doing each multiplication separately: $a(b + c) = ab + ac$.
$0$ is the identity element for addition because any number plus $0$ remains unchanged: $a + 0 = a$. Similarly, $1$ is the identity element for multiplication: $a \times 1 = a$.