The associative property refers to the way numbers are grouped in an operation. In mathematics, this property states that when adding or multiplying several numbers, the way the numbers are grouped (associated) does not change the result. The associative property applies to addition and multiplication, but not to subtraction or division.
Associative Property Formulas
The formulas for the associative property are:
- For addition: (a + b) + c = a + (b + c)
- For multiplication: (a × b) × c = a × (b × c)
Example 1: Associative Property with Addition
Show that (2 + 3) + 4 = 2 + (3 + 4).
Calculation: (2 + 3) + 4 = 5 + 4 = 9 and 2 + (3 + 4) = 2 + 7 = 9. Both sides equal 9, demonstrating the associative property.
Example 2: Associative Property with Multiplication
Show that (3 × 2) × 5 = 3 × (2 × 5).
Calculation: (3 × 2) × 5 = 6 × 5 = 30 and 3 × (2 × 5) = 3 × 10 = 30. Both sides equal 30, demonstrating the associative property.
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