Question

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
(14)( )(2)=(7)( )(14)

Answer 1

To make the two algebraic expressions equivalent using the Commutative Property, we can rearrange the numbers so that both sides of the equation match.

The original expressions are:

\[
(14)(\_)(2) = (7)(\_)(14)
\]

Using the Commutative Property, we know that the order of multiplication does not affect the product.

Let's fill in the blanks:

1. For the first blank on the left side, we need a number that when multiplied by 14 and 2 gives the same result as the right side. Since \(14\) and \(7\) appear, the missing number must be \(1\) (since \(7 \times 2 = 14\)) because \(14 = 7 \times 2\).

2. For the second blank on the right side, we have \(2\) that can multiply with \(7\) to maintain equivalence.

Thus, we can fill in the blanks as:

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

So, the complete equation is:

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

This way, both expressions are now equivalent using the Commutative Property.