What property of multiplication is illustrated by the manipulatives of the accompanying diagrams? \begin{tabular}{|l|l|l|l|l|l|l|l|l|}\hline DG & DG & DG & DG & DG & DG & DG & DG & DG \\ Dark Green \( (\mathrm{DG})=6 \)-rod \\ A. The associative property \\ B. The commutative property \\ C. The multiplication-by-zero property \\ D. The multiplicative identity property of one \\ Choose the correct answer below. \\ E. The closure property \\ F. The distributive property of multiplication over addition \end{tabular} :

To determine which property of multiplication is illustrated by the manipulatives of the accompanying diagrams, we need to analyze the options provided in relation to the concept of multiplication. 1. **Associative Property**: This property states that the way in which numbers are grouped in multiplication does not change the product. For example, \((a \times b) \times c = a \times (b \times c)\). 2. **Commutative Property**: This property states that the order in which two numbers are multiplied does not change the product. For example, \(a \times b = b \times a\). 3. **Multiplication-by-Zero Property**: This property states that any number multiplied by zero equals zero. For example, \(a \times 0 = 0\). 4. **Multiplicative Identity Property of One**: This property states that any number multiplied by one remains unchanged. For example, \(a \times 1 = a\). 5. **Closure Property**: This property states that the product of any two numbers in a given set is also a member of that set. 6. **Distributive Property of Multiplication over Addition**: This property states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products. For example, \(a \times (b + c) = a \times b + a \times c\). Given that the problem mentions "manipulatives of the accompanying diagrams" and refers to a specific rod (Dark Green \( (\mathrm{DG})=6 \)-rod), it suggests a visual representation of multiplication. If the diagrams show how groups of rods can be rearranged or combined without changing the total, it would illustrate the **commutative property** or the **associative property**. However, without specific details about the diagrams, we cannot definitively choose between these two. If the diagrams show that the arrangement of the rods does not affect the total count, it would indicate the **commutative property**. Thus, the most likely answer, based on the context of manipulatives and the nature of multiplication, is: **B. The commutative property**.