To use the Commutative Property to fill in the blanks so that the two algebraic expressions are equivalent, we want to ensure that both sides of the equation can be rearranged to match each other.
The expression on the left is:
\( (14) \cdot () \cdot (2) \)
The expression on the right is:
\( (7) \cdot () \cdot (14) \)
Notice that both expressions contain the number \( 14 \) and involve multiplication. If we rearrange the left side to match the right side, we can position the factors appropriately.
To make the two expressions equivalent:
- We can fill in \( 1 \) for the first blank (since multiplying by 1 does not change the value).
- In the second blank, we can also place \( 1 \).
Now let's write them out:
Left side:
\( (14) \cdot (1) \cdot (2) = (14) \cdot (2) \cdot (1) \) (using the Commutative Property)
Right side:
\( (7) \cdot (4) \cdot (14) = (7) \cdot (14) \cdot (4) \) (we can derive \( 2 = 14/7 \))
So this leads to the completed expressions:
Answer:
(14)(1)(2)=(7)(4)(14)