To determine which property is represented by the given equation \((8 \times 5) \times 6.75 = 8 \times (5 \times 6.75)\), we need to analyze the characteristics of this equation and match them with the properties of mathematical operations.
Let's examine the equation step by step:
1. The equation involves only multiplication.
2. It shows that the way the numbers are grouped (with parentheses) does not affect the final product.
Now, let's review the properties mentioned in the question:
a. Identity Property of Addition:
- This property states that any number plus zero is the number itself: \(a + 0 = a\).
- This property does not apply here since the equation deals with multiplication, not addition.
b. Commutative Property of Multiplication:
- This property states that the order in which two numbers are multiplied does not change the product: \(a \times b = b \times a\).
- In the given equation, the order of multiplication changes within the groupings but not the order of the factors themselves.
c. Distributive Property:
- This property combines multiplication and addition: \(a \times (b + c) = a \times b + a \times c\).
- The given equation does not involve addition, so this property is not applicable here.
d. Associative Property of Multiplication:
- This property states that the way in which factors are grouped in a multiplication problem does not change the product: \((a \times b) \times c = a \times (b \times c)\).
- The given equation exactly matches this description, showing different groupings of the same multiplicative factors, yet yielding the same product.
After reviewing the properties, we can conclude that the correct answer is:
d. Associative Property of Multiplication
