Question

Structures of Expressions Online Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 4 of 174 of 17 Items Question Which expressions correctly demonstrate the Commutative Property?(1 point) Responses 3x(9y+6)=(3x+9y)⋅6 3 x left parenthesis 9 y plus 6 right parenthesis equals left parenthesis 3 x plus 9 y right parenthesis times 6 3x⋅9y⋅6=162xy 3 x times 9 y times 6 equals 162 x y 3x⋅9y⋅6=9y+6+3x 3 x times 9 y times 6 equals 9 y plus 6 plus 3 x 3x⋅9y⋅6=9y⋅6⋅3x

Answer 1

The Commutative Property states that the order of addition or multiplication does not change the result. In other words, for any numbers \( a \) and \( b \):

- \( a + b = b + a \) (Addition)
- \( a \cdot b = b \cdot a \) (Multiplication)

Looking at the provided responses, we can evaluate them to see which correctly demonstrates the Commutative Property:

1. **3x(9y+6)=(3x+9y)⋅6** – This expression does not demonstrate the Commutative Property because it is an equation involving distribution and addition, not simply a rearrangement of terms.

2. **3x⋅9y⋅6=162xy** – This expression does not explicitly demonstrate the Commutative Property, but it shows the result of multiplying the terms together, not the rearrangement.

3. **3x⋅9y⋅6=9y+6+3x** – This expression does not demonstrate the Commutative Property as it involves addition rather than a rearrangement of the multiplied terms.

4. **3x⋅9y⋅6=9y⋅6⋅3x** – This expression demonstrates the Commutative Property for multiplication, as it shows a rearrangement of the order in which the numbers are multiplied.

Thus, the response that correctly demonstrates the Commutative Property is:

**3x⋅9y⋅6=9y⋅6⋅3x**.