Your proof that \( y \cdot 3x \) is equivalent to \( 3xy \) using the Commutative Property is clear and correct. Here’s a brief recap and more details to reinforce the steps:
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Starting with the expression: \[ y \cdot 3x \] we can rewrite it by factoring out the constant 3: \[ y \cdot 3x = 3 \cdot y \cdot x \]
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Now, we can apply the Commutative Property of multiplication, which states that the order of multiplication does not affect the product. This allows us to rearrange the factors: \[ 3 \cdot y \cdot x = 3 \cdot x \cdot y \]
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Finally, we can write this in a compact form: \[ 3 \cdot x \cdot y = 3xy \]
Thus, we have shown that: \[ y \cdot 3x = 3xy \] This confirms that \( y \cdot 3x \) and \( 3xy \) are indeed equivalent expressions, validating the use of the Commutative Property in multiplication. Great job!