Simplify: \(-\frac{7}{6} + \frac{4}{9} \div \frac{5}{3} \times \frac{1}{16}\)
-23/20
Expression: \(-\frac{7}{6} + \frac{4}{9} \div \frac{5}{3} \times \frac{1}{16}\)
- Start with the division operation: \(\frac{4}{9} \div \frac{5}{3} = \frac{4}{9} \times \frac{3}{5} = \frac{4 \times 3}{9 \times 5} = \frac{12}{45}\). Simplify \(\frac{12}{45}\) to \(\frac{4}{15}\).
- Next, perform the multiplication: \(\frac{4}{15} \times \frac{1}{16} = \frac{4 \times 1}{15 \times 16} = \frac{4}{240}\). Simplify \(\frac{4}{240}\) to \(\frac{1}{60}\).
- The expression is now: \(-\frac{7}{6} + \frac{1}{60}\).
- Find a common denominator: The least common multiple (LCM) of 6 and 60 is 60.
- Convert \(-\frac{7}{6}\): \(-\frac{7}{6} = -\frac{7 \times 10}{6 \times 10} = -\frac{70}{60}\).
- The expression becomes: \(-\frac{70}{60} + \frac{1}{60} = \frac{-70 + 1}{60} = \frac{-69}{60}\).
- Simplify the fraction: \(\frac{-69}{60}\) can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3. \(= \frac{-69 \div 3}{60 \div 3} = \frac{-23}{20}\).
Thus, the simplified result is \(\frac{-23}{20}\), matching option -23/20.
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