To simplify the expression \(9/4/7/15 \times 14 \times 5 \times 6\), we can first rewrite the fractions and multiplications clearly:
\[ \frac{9}{4} \div 7 \div 15 \times 14 \times 5 \times 6 \]
Let’s break this down step by step.
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Combining Divisions: \[ \frac{9}{4} \div 7 = \frac{9}{4} \times \frac{1}{7} = \frac{9}{28} \] Now we divide that result by 15: \[ \frac{9}{28} \div 15 = \frac{9}{28} \times \frac{1}{15} = \frac{9}{420} \]
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Simplifying \( \frac{9}{420} \): We can simplify \( \frac{9}{420} \):
- The greatest common divisor (GCD) of 9 and 420 is 3. \[ \frac{9 \div 3}{420 \div 3} = \frac{3}{140} \]
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Now multiply the fractions by 14, 5, and 6: \[ \frac{3}{140} \times 14 \times 5 \times 6 \]
First, multiply \( \frac{3}{140} \times 14 \): \[ \frac{3 \times 14}{140} = \frac{42}{140} = \frac{3}{10} \quad \text{(simplifying by dividing both by 14)} \]
Now, we have \( \frac{3}{10} \times 5 \): \[ \frac{3 \times 5}{10} = \frac{15}{10} = \frac{3}{2} \quad \text{(simplifying by dividing both by 5)} \]
Finally, multiply \( \frac{3}{2} \times 6 \): \[ \frac{3 \times 6}{2} = \frac{18}{2} = 9 \]
Thus, the final result is:
\[ \boxed{9} \]