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=9y⋅6⋅3x 3 x times 9 y times 6 equals 9 y times 6 times 3 x 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 Remaining Attempts : 3

Answer 1

The Commutative Property states that the order in which you add or multiply numbers does not change the result. In the context of multiplication, this means that \( a \cdot b = b \cdot a \).

Let's analyze the provided expressions:

1. \( 3x \cdot 9y \cdot 6 = 9y + 6 + 3x \): This is incorrect because the left side is a product, while the right side is a sum.

2. \( 3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x \): This is correct. It demonstrates the Commutative Property because the product remains the same regardless of the order of the factors.

3. \( 3x(9y + 6) = (3x + 9y) \cdot 6 \): This does not demonstrate the Commutative Property; instead, it applies the distributive property incorrectly.

4. \( 3x \cdot 9y \cdot 6 = 162xy \): While this is mathematically correct (since \( 3 \cdot 9 \cdot 6 = 162 \)), it doesn't demonstrate the Commutative Property.

The only expression that correctly demonstrates the Commutative Property is:

\( 3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x \).