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Let's solve the given mathematical expression:

\[
\frac{-3}{17} \times \frac{2}{3} + \frac{2}{3} \times \frac{-14}{17}
\]

### Step-by-Step Solution:

1. **First part: \(\frac{-3}{17} \times \frac{2}{3}\)**:
   - Multiply the numerators: \(-3 \times 2 = -6\)
   - Multiply the denominators: \(17 \times 3 = 51\)
   - So, \(\frac{-3}{17} \times \frac{2}{3} = \frac{-6}{51}\)

2. **Second part: \(\frac{2}{3} \times \frac{-14}{17}\)**:
   - Multiply the numerators: \(2 \times (-14) = -28\)
   - Multiply the denominators: \(3 \times 17 = 51\)
   - So, \(\frac{2}{3} \times \frac{-14}{17} = \frac{-28}{51}\)

3. **Add the two results**:
   - \(\frac{-6}{51} + \frac{-28}{51} = \frac{-6 - 28}{51} = \frac{-34}{51}\)

4. **Simplify the final result**:
   - \(\frac{-34}{51}\) cannot be simplified further as 34 and 51 have no common factors other than 1.

Thus, the final answer is:

\[
\frac{-34}{51}
\]

Would you like a deeper explanation or have any questions? Here are some related questions you could explore:

1. How do you multiply two fractions?
2. What are the rules for adding fractions with the same denominator?
3. How can you simplify a fraction?
4. What happens when both fractions being multiplied are negative?
5. How can you convert improper fractions to mixed numbers?

**Tip:** When multiplying fractions, always simplify the numerators and denominators as early as possible to avoid large numbers!

Learn how to solve the fraction expression (-3/17) * (2/3) + (2/3) * (-14/17) with a step-by-step solution. This covers key concepts in multiplying and adding fractions, perfect for students in Grades 6-8.

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