Question

Which expressions correctly demonstrate the Commutative Property?(1 point) Responses 3x⋅9y⋅6=9y⋅6⋅3x3𝑥⋅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)⋅63𝑥(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=162xy3𝑥⋅9𝑦⋅6=162xy 3 x times 9 y times 6 equals 162 x y 3x⋅9y⋅6=9y+6+3x

Answer 1

The Commutative Property states that the order in which you add or multiply numbers does not change the sum or product. For multiplication, this means that \( a \cdot b = b \cdot a \) and for addition, this means that \( a + b = b + a \).

Given the responses:

1. \( 3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x \) (Correct: This demonstrates the Commutative Property for multiplication.)
2. \( 3x(9y + 6) = (3x + 9y) \cdot 6 \) (Incorrect: This demonstrates the Distributive Property, not the Commutative Property.)
3. \( 3x \cdot 9y \cdot 6 = 162xy \) (Incorrect: This is just an equation representing a calculation, not an expression demonstrating commutativity.)
4. \( 3x \cdot 9y \cdot 6 = 9y + 6 + 3x \) (Incorrect: This does not properly represent multiplication and is not an example of commutativity.)

Thus, the first expression, \( 3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x \), is the only correct example demonstrating the Commutative Property.