Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?

Question

3(b10+4)=3(4+b10)3
z11⋅2=z11+2
2(b10+z11)=(b10+z11)⋅2
11(b+z)=11b+11z

Answer 1

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \cdot b = b \cdot a \).

Given the options:

1. 3(b10 + 4) = 3(4 + b10)3
   This expression does not correctly demonstrate the Commutative Property since it has an incorrect structure and misuses operators.

2. z11 ⋅ 2 = z11 + 2
   This statement is incorrect, as it suggests multiplication equals addition, which violates basic arithmetic principles.

3. 2(b10 + z11) = (b10 + z11) ⋅ 2
   This is the correct use of the Commutative Property. It shows that multiplying the sum \( (b10 + z11) \) by 2 can be expressed in either order.

4. 11(b + z) = 11b + 11z
   This expression illustrates the Distributive Property, not the Commutative Property.

Thus, the correct answer demonstrating the use of the Commutative Property of Multiplication is:

2(b10 + z11) = (b10 + z11) ⋅ 2.