Questions: Which of these expressions are equivalent to 25 * 18 * 12 by the Commutative Property of Multiplication? What is the value of each of these equivalent expressions? 450 * 12 18 * 300 25 * 12 * 18 18 * 25 * 12 Select all of the expressions that are equivalent to 25 * 18 * 12 by the Commutative Property of Multiplication. A. 450 * 12 B. 25 * 12 * 18 C. 18 * 25 * 12 D. 18 * 300 What is the value of each of the equivalent expressions?

Solution Steps

To determine which expressions are equivalent to \(25 \cdot 18 \cdot 12\) using the Commutative Property of Multiplication, we need to check if rearranging the factors results in the same product. The Commutative Property states that the order of multiplication does not affect the product. We will calculate the product of each expression and compare it to the original expression.

First, we calculate the value of the original expression \(25 \cdot 18 \cdot 12\).

\[ 25 \cdot 18 \cdot 12 = 5400 \]

Next, we evaluate each of the given expressions to see if they are equivalent to the original expression.

• Expression A: \(450 \cdot 12\) \[ 450 \cdot 12 = 5400 \]

• Expression B: \(25 \cdot 12 \cdot 18\) \[ 25 \cdot 12 \cdot 18 = 5400 \]

• Expression C: \(18 \cdot 25 \cdot 12\) \[ 18 \cdot 25 \cdot 12 = 5400 \]

• Expression D: \(18 \cdot 300\) \[ 18 \cdot 300 = 5400 \]

All the given expressions evaluate to the same value as the original expression, \(5400\). Therefore, they are all equivalent by the Commutative Property of Multiplication.

Final Answer