Question

Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?(1 point)%0D%0AResponses%0D%0A%0D%0A11(b+z)=11b+11z%0D%0A11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z%0D%0A%0D%0A3(b10+4)=3(4+b10)3%0D%0A3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3%0D%0A%0D%0Az11⋅2=z11+2%0D%0Az superscript 11 baseline times 2 equals z superscript 11 baseline plus 2%0D%0A%0D%0A2(b10+z11)=(b10+z11)⋅2

Answer 1

The Commutative Property of Multiplication states that changing the order of the factors does not change the product.

Let's evaluate the provided options:

1. 11(b + z) = 11b + 11z: This is an example of the Distributive Property, not the Commutative Property.

2. 3(b^10 + 4) = 3(4 + b^10): This expresses the Commutative Property in the part where it shows 4 + b^10 instead of b^10 + 4, but the multiplication by 3 doesn't change.

3. z^11 · 2 = z^11 + 2: This is incorrect; it does not reflect any property of multiplication.

4. 2(b^10 + z^11) = (b^10 + z^11) · 2: This expression shows the Associative Property and the Distributive Property, not the Commutative Property.

The one that effectively demonstrates the Commutative Property of Multiplication is the second one (implicitly), as you can see that mixing the order in the parentheses does not affect multiplication, even though it may not explicitly exhibit the property in the traditional sense.

Thus, none of the options clearly showcase the Commutative Property on its own, but the closest one demonstrating it could be option 2.

To directly answer, none clearly and explicitly demonstrate the Commutative Property of Multiplication as standalone expressions.