Let's simplify the expression step by step:

\[
\left( \frac{-4}{5} \right) \times \left( \frac{3}{7} \right) \times \left( \frac{15}{16} \right) \times \left( \frac{-14}{9} \right)
\]

### Step 1: Multiply the numerators
Multiply the numerators first:
\[
(-4) \times 3 \times 15 \times (-14) = (-4 \times 15) \times (3 \times -14) = (-60) \times (-42) = 2520
\]

### Step 2: Multiply the denominators
Now multiply the denominators:
\[
5 \times 7 \times 16 \times 9 = (5 \times 16) \times (7 \times 9) = 80 \times 63 = 5040
\]

### Step 3: Simplify the fraction
Now, simplify the fraction:
\[
\frac{2520}{5040}
\]

Divide both the numerator and denominator by their greatest common divisor, which is 2520:
\[
\frac{2520 \div 2520}{5040 \div 2520} = \frac{1}{2}
\]

Thus, the simplified expression is:

\[
\boxed{\frac{1}{2}}
\]

Would you like more details on any step or further explanations?

Here are 5 related questions you might be interested in:
1. How do you find the greatest common divisor of two numbers?
2. What are the rules for multiplying fractions?
3. How do you simplify more complex fractions?
4. How does multiplying negative numbers affect the result?
5. What strategies can be used to simplify large products of fractions?

**Tip:** Always check if factors in the numerator and denominator can be canceled early to simplify calculations!

Learn how to simplify the fraction expression (-4/5) * (3/7) * (15/16) * (-14/9) step-by-step. This solution involves multiplying fractions, dealing with negative numbers, and simplifying using the greatest common divisor (GCD). Perfect for students in Grades 6-8.

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