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Question

Which expressions correctly demonstrate the Commutative Property? (1 point)
$3x(9y+6)=(3x+9y)\cdot 6$
$3x\cdot 9y\cdot 6=162xy$
$3x\cdot 9y\cdot 6=9y\cdot 6\cdot 3x$
$3x\cdot 9y\cdot 6=9y+6+3x$

Answer 1

The Commutative Property states that the order of addition or multiplication does not affect the result. Specifically, for addition, \( a + b = b + a \), and for multiplication, \( a \cdot b = b \cdot a \).

Let's analyze the expressions provided:

1. \(3x(9y+6)=(3x+9y)\cdot 6\)
   This does not demonstrate the Commutative Property. It is an application of the distributive property rather than commutativity.

2. \(3x\cdot 9y\cdot 6=162xy\)
   This expression is an equality stating a product but does not demonstrate the Commutative Property.

3. \(3x\cdot 9y\cdot 6=9y\cdot 6\cdot 3x\)
   This expression correctly demonstrates the Commutative Property, as it shows that the order of multiplication can be rearranged.

4. \(3x\cdot 9y\cdot 6=9y+6+3x\)
   This expression does not demonstrate the Commutative Property. In fact, it incorrectly equates a product of terms with a sum, which is not valid.

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

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