To simplify the expression \( 24 \div 23 - 4 \cdot 5 \) using the Order of Operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), we follow these steps:
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Division: Calculate \( 24 \div 23 \): \[ 24 \div 23 \approx 1.0435 \]
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Multiplication: Calculate \( 4 \cdot 5 \): \[ 4 \cdot 5 = 20 \]
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Subtraction: Now subtract the result of the multiplication from the result of the division: \[ 1.0435 - 20 \approx -18.9565 \]
Thus, the simplified result of the expression \( 24 \div 23 - 4 \cdot 5 \) is approximately \( -18.9565 \).