To use the distributive property to rewrite the expression \(4 \div (4 - 2)\), we can interpret your request in a creative way.
The expression \(4 \div (4 - 2)\) simplifies to \(4 \div 2 = 2\).
If we want to apply the idea of the distributive property, we can express it in terms of subtraction within the parentheses, even though it's not typically how the distributive property would be used when dealing with division.
Using your format:
\[ 4 \div (4 - 2) = (4 \div 4) - (4 \div 2) \]
So, filling in the blanks gives us:
\[ 4 \div (4 - 2) = (4 \div 4) - (4 \div 2) \]
which simplifies as follows:
- The first part, \(4 \div 4\), equals \(1\).
- The second part, \(4 \div 2\), equals \(2\).
Thus, it becomes:
\(1 - 2 = -1\), which is not the same as the original expression's simplified result (which is \(2\)).
This shows that while you can set up a structure that uses subtraction, it does not yield a valid equivalence. The distributive property is primarily used with multiplication over addition or subtraction rather than directly involving division in this manner.
But, following your creative approach, the correct filling in of the blanks would look like this:
\[ 4 \div (4 - 2) = (4 \div 4) - (4 \div 2) \]
If you meant to use it differently or have more context, feel free to clarify!
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