Let's solve the expression step by step, applying the properties of operations with signed numbers.
The original expression is: \[ (-3) \times \left(\frac{4}{3}\right) \div \left(-\frac{2}{5}\right) \times \left(\frac{1}{6}\right) \]
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Multiplication and Division of Signed Numbers:
- Multiply first: \[ (-3) \times \left(\frac{4}{3}\right) = -\frac{12}{3} = -4 \]
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Next, divide:
- Now we have: \[ -4 \div \left(-\frac{2}{5}\right) \]
- Dividing by a negative number involves changing signs: \[ -4 \div \left(-\frac{2}{5}\right) = -4 \times \left(-\frac{5}{2}\right) = 4 \times \frac{5}{2} = \frac{20}{2} = 10 \]
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Finally, multiply:
- Now, we will multiply by \(\frac{1}{6}\): \[ 10 \times \left(\frac{1}{6}\right) = \frac{10}{6} = \frac{5}{3} \]
At this point, \(\frac{5}{3}\) can be expressed as a mixed number: \[ \frac{5}{3} = 1 \frac{2}{3} \]
Therefore, the final result of the expression is: \[ \boxed{1 \frac{2}{3}} \]
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