To solve the expression \((-2) \times \left(\frac{1}{5}\right) \times \left(\frac{2}{3}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{3}{4}\right)\), we can follow the steps systematically.
- Multiply the whole numbers and fractions step by step. We can rearrange and group terms for easier calculation.
Let's first calculate: \[ (-2) \times \left(-\frac{5}{6}\right) \quad \text{and} \quad \left(\frac{1}{5}\right) \times \left(\frac{2}{3}\right) \times \left(\frac{3}{4}\right) \]
-
Calculate the product of the whole numbers: \[ (-2) \times (-\frac{5}{6}) = \frac{10}{6} = \frac{5}{3} \]
-
Calculate the product of the fractions: \[ \left(\frac{1}{5}\right) \times \left(\frac{2}{3}\right) = \frac{2}{15} \]
\[ \frac{2}{15} \times \left(\frac{3}{4}\right) = \frac{2 \times 3}{15 \times 4} = \frac{6}{60} = \frac{1}{10} \]
- Now combine the results from step 2 and step 3: \[ \frac{5}{3} \times \frac{1}{10} = \frac{5 \times 1}{3 \times 10} = \frac{5}{30} = \frac{1}{6} \]
Therefore, the final answer is: \[ \frac{1}{6} \]
So, the correct answer is 1/6.
1 answer