The associative property states that when you add or multiply numbers, changing how
they are grouped with parentheses does not change the final answer. The associative
property works for addition and multiplication only. Does not work for subtraction or
division because grouping changes the result.
Core Rules
Addition: (a + b) + c = a + (b + c)
Multiplication: (a • b) • c = a • (b • c)
Keep in mind, only the grouping changes, not the order of the numbers. (If you change
the order, it is the commutative property)
Examples
Addition: (2 + 3) + 4 = 5 + 4 = 9, and 2 + (3 + 4) = 2 + 7 = 9
Multiplication: (2 • 5) • 3 = 10 • 3 = 30, and 2 • (5 • 3) = 2 • 15 = 30
Examples with Variables
Addition: x + (y + z) = (x + y) + z
Multiplication: 2 • (3x) = (2 • 3) • x = 6x
they are grouped with parentheses does not change the final answer. The associative
property works for addition and multiplication only. Does not work for subtraction or
division because grouping changes the result.
Core Rules
Addition: (a + b) + c = a + (b + c)
Multiplication: (a • b) • c = a • (b • c)
Keep in mind, only the grouping changes, not the order of the numbers. (If you change
the order, it is the commutative property)
Examples
Addition: (2 + 3) + 4 = 5 + 4 = 9, and 2 + (3 + 4) = 2 + 7 = 9
Multiplication: (2 • 5) • 3 = 10 • 3 = 30, and 2 • (5 • 3) = 2 • 15 = 30
Examples with Variables
Addition: x + (y + z) = (x + y) + z
Multiplication: 2 • (3x) = (2 • 3) • x = 6x
