Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.

Question

(14)
(
)(2)=(7)
(
)(14)

Answer 1

To fill in the blanks using the Commutative Property, we know that the order of multiplication does not affect the result. We can set up the equation based on the structure you've provided:

Starting from the left side: \((14)(__)(2)=(7)(__)(14)\)

To focus on the variable blanks, let's express the left side of the equation:

\[ (14) \times (1) \times (2) = (7) \times (4) \times (14) \]

Now we can fill in the blanks with \(1\) and \(4\) respectively. So we have:

\[ (14)(1)(2) = (7)(4)(14) \]

This gives us the complete filled-in equation as:

\[ (14)(1)(2) = (7)(4)(14) \]

Hence, the filled-in blanks are:

\((1)\) and \((4)\).