Answer :
Answer:
Step-by-step explanation:To solve the problem \(-\frac{6}{7} \times \frac{4}{9} \times \frac{15}{18} \times \left(-\frac{21}{14}\right) = \frac{10}{21}\), we need to simplify each fraction and check if their product equals \(\frac{10}{21}\).
Let's simplify each fraction step by step:
1. **Simplify \(\frac{15}{18}\):**
\[
\frac{15}{18} = \frac{15 \div 3}{18 \div 3} = \frac{5}{6}
\]
2. **Simplify \(-\frac{21}{14}\):**
\[
-\frac{21}{14} = -\frac{21 \div 7}{14 \div 7} = -\frac{3}{2}
\]
Now substitute these simplified fractions into the original expression:
\[
-\frac{6}{7} \times \frac{4}{9} \times \frac{5}{6} \times \left(-\frac{3}{2}\right)
\]
Next, multiply these fractions step by step:
- Multiply \(\frac{6}{7} \times \frac{4}{9}\):
\[
\frac{6 \times 4}{7 \times 9} = \frac{24}{63} = \frac{8}{21}
\]
- Multiply \(\frac{8}{21} \times \frac{5}{6}\):
\[
\frac{8 \times 5}{21 \times 6} = \frac{40}{126} = \frac{20}{63}
\]
- Multiply \(\frac{20}{63} \times -\frac{3}{2}\):
\[
\frac{20 \times -3}{63 \times 2} = \frac{-60}{126} = -\frac{30}{63} = -\frac{10}{21}
\]
Therefore, the left-hand side of the equation simplifies to \(-\frac{10}{21}\), not \(\frac{10}{21}\) as given in the problem statement. There seems to be a contradiction here since the calculated result is negative. Double-checking all calculations confirms that the left-hand side simplifies to \(-\frac{10}{21}\) rather than \(\frac{10}{21}\).
Thus, the statement \(-\frac{6}{7} \times \frac{4}{9} \times \frac{15}{18} \times \left(-\frac{21}{14}\right) = \frac{10}{21}\) is incorrect based on the calculations performed.