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:

Question

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:
1. Starting with the expression:
$$
y \cdot 3x
$$
we can rewrite it by factoring out the constant 3:
$$
y \cdot 3x = 3 \cdot y \cdot x
$$

2. 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:
$$
3 \cdot y \cdot x = 3 \cdot x \cdot y
$$

3. 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.
make it smaller

GPT-4o mini · Answer

To show that $ y \cdot 3x $ is equivalent to $ 3xy $, we can use the Commutative Property of multiplication: 1. Start with the expression: $$ y \cdot 3x = y \cdot (3 \cdot x) $$ 2. Use the Commutative Property to rearrange the factors: $$ y \cdot (3 \cdot x) = 3 \cdot (y \cdot x) = 3xy $$ Thus, we conclude: $$ y \cdot 3x = 3xy $$ This confirms that the two expressions are equivalent.

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: