To use the Commutative Property, we need to rearrange the multiplication in the two algebraic expressions to make them equivalent.
The expression on the left is \( (14)(__)(2) \) and the expression on the right is \( (7)(__)(14) \).
To find a suitable value for the blanks, we can simplify both expressions.
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First, simplify the right-hand side: \[ (7)(14) = 98 \] So we need to make the left-hand side equal to 98.
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Now, simplify the left-hand side: \[ (14)(__)(2) = 28(__) \] We need to find \( x \) such that: \[ 28x = 98 \] Dividing both sides by 28 gives us: \[ x = \frac{98}{28} = 3.5 \]
Now we substitute the value into the blank in the left-hand side expression: Thus, the completed expressions are: \[ (14)(3.5)(2) = (7)(__)(14) \]
- Now, we need to determine what goes in the blank on the right. We can calculate: \[ (7)(__)(14) = 98 \] To make this equation true, the missing term should equal: \[ __ = \frac{98}{(7)(14)} = 1 \]
So the final filled-in expression is: \[ (14)(3.5)(2) = (7)(1)(14) \]
Final answer: \( (14)(3.5)(2) = (7)(1)(14) \).
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