Question

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

Answer 1

To use the Commutative Property to fill in the blanks so that the two algebraic expressions are equivalent, we can rearrange the order of multiplication.

Given the first expression: \((14)(\_\_)(2)\)

And the second expression: \((7)(\_\_)(14)\)

First, let's simplify the expressions. We know that:

1. In the second expression, \(7\) can be multiplied by \(2\) to give \(14\) (since \(7 \times 2 = 14\)).
2. So, to make the two expressions equivalent, we can fill in the first blank with \(1\) (as multiplying by \(1\) does not change the product).

Now let's check:

The first expression becomes:
\[
(14)(1)(2) = 28
\]

The second expression:
Choosing \(2\) for the second blank:
\[
(7)(2)(14) = (7 \times 2) \times 14 = 14 \times 14 = 196
\]

This doesn't work. Apologies for the oversight. Let's redo it with \(x\) as a placeholder and use \(\frac{1}{7}\).

Now we can fill in the blanks as follows:
\[
(14)(\frac{1}{7})(2) = (7)(4)(14)
\]
because \(14 \times \frac{1}{7} = 2\), and here we have \(2\) in the end.

So, the complete answer is:
\((14)(\frac{1}{7})(2) = (7)(4)(14)\).

Thus:
**Fill in the blanks:** \( \frac{1}{7} \) and \( 4 \).