To simplify the expression \( 3(42 + 32 \div 4 - 5) \), we first need to solve the calculation inside the parentheses.
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Calculate \( 32 \div 4 \):
\[ 32 \div 4 = 8 \]
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Substitute it back into the expression:
\[ 3(42 + 8 - 5) \]
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Now simplify \( 42 + 8 - 5 \):
\[ 42 + 8 = 50 \] \[ 50 - 5 = 45 \]
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Thus, we have:
\[ 3(45) \]
Therefore, the quotient that must be found to simplify the expression is \( 32 \div 4 \).
The correct answer is:
32 ÷ 4.