Simplify: 60 - {(-8) × (-16 - 19 - 2)} ÷ [5 × {2 + (-1) × (-1)}]
$\frac{604}{15}$
To solve the expression \(60 - \{(-8) \times (-16 - 19 - 2)\} \div [5 \times \{2 + (-1) \times (-1)\}]\), we need to follow the order of operations (BODMAS/BIDMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction).
- First, simplify the expression inside the innermost brackets: \(-16 - 19 - 2\).
- \(-16 - 19 = -35\)
- \(-35 - 2 = -37\)
- Now, solve the expression \((-8) \times (-37)\).
- \((-8) \times (-37) = 296\) (since the product of two negative numbers is positive)
- Simplify inside the brackets: \((-1) \times (-1)\).
- \((-1) \times (-1) = 1\)
- Calculate inside the bracket: \(2 + 1 = 3\).
- Now, multiply by 5: \(5 \times 3 = 15\).
- Perform the division: \(296 \div 15\).
- \(296 \div 15 = \frac{296}{15}\) (Keep it as a fraction for precise calculation in subsequent steps)
- Convert \(60\) to a fraction with a denominator of 15 to perform the subtraction:
- \(60 = \frac{60 \times 15}{15} = \frac{900}{15}\)
- Subtract the fractions: \(\frac{900}{15} - \frac{296}{15}\).
- \(\frac{900}{15} - \frac{296}{15} = \frac{900 - 296}{15} = \frac{604}{15}\)
Therefore, the simplified value of the expression is \(\frac{604}{15}\).
The correct answer is \(\frac{604}{15}\).
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