Question

Which expressions correctly demonstrate the Commutative Property?(1 point)
Responses

3x⋅9y⋅6=9y+6+3x
3 x times 9 y times 6 equals 9 y plus 6 plus 3 x

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 times 6 times 3 x

3x(9y+6)=(3x+9y)⋅6

Answer 1

The Commutative Property states that the order in which two numbers are added or multiplied does not change the result. This property applies to addition and multiplication.

Let's evaluate the provided expressions for the Commutative Property:

1. **3x ⋅ 9y ⋅ 6 = 9y + 6 + 3x**: This is incorrect. The left side is a product, while the right side is a sum.

2. **3x ⋅ 9y ⋅ 6 = 162xy**: This is an equality that is true (since \(3 \cdot 9 \cdot 6 = 162\)), but it does not demonstrate the Commutative Property.

3. **3x ⋅ 9y ⋅ 6 = 9y ⋅ 6 ⋅ 3x**: This is correct and demonstrates the Commutative Property because it rearranges the factors of multiplication.

4. **3x(9y + 6) = (3x + 9y) ⋅ 6**: This is incorrect. It does not demonstrate the Commutative Property but rather the Distributive Property.

The valid expression that demonstrates the Commutative Property is:

**3x ⋅ 9y ⋅ 6 = 9y ⋅ 6 ⋅ 3x**.