https://file.aiquickdraw.com/mathbot/file/1728344764592l6c577cl.jpg

Let's solve the expression step by step. The expression is:

\[
\frac{2}{5} \times \left(-\frac{3}{7}\right) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5}
\]

### Step 1: Multiply each term separately.

1. **First Term**: \(\frac{2}{5} \times \left(-\frac{3}{7}\right)\)

\[
\frac{2}{5} \times \left(-\frac{3}{7}\right) = -\frac{6}{35}
\]

2. **Second Term**: \(\frac{1}{6} \times \frac{3}{2}\)

\[
\frac{1}{6} \times \frac{3}{2} = \frac{3}{12} = \frac{1}{4}
\]

3. **Third Term**: \(\frac{1}{14} \times \frac{2}{5}\)

\[
\frac{1}{14} \times \frac{2}{5} = \frac{2}{70} = \frac{1}{35}
\]

### Step 2: Combine the results.

\[
-\frac{6}{35} - \frac{1}{4} + \frac{1}{35}
\]

### Step 3: Find a common denominator.

The least common denominator (LCD) of 35 and 4 is 140. We convert each fraction:

- \(-\frac{6}{35} = -\frac{24}{140}\)
- \(-\frac{1}{4} = -\frac{35}{140}\)
- \(\frac{1}{35} = \frac{4}{140}\)

### Step 4: Combine the fractions.

\[
-\frac{24}{140} - \frac{35}{140} + \frac{4}{140} = \frac{-24 - 35 + 4}{140}
\]

\[
= \frac{-55}{140}
\]

### Step 5: Simplify the fraction.

\[
\frac{-55}{140} = \frac{-11}{28}
\]

### Final Answer:

\[
\boxed{-\frac{11}{28}}
\]

Would you like further details or explanations on any specific step? Here are some related questions:

1. How do you find the least common denominator for fractions?
2. What are the rules for multiplying fractions with negative signs?
3. How can you simplify fractions efficiently?
4. What methods can be used to solve expressions involving multiple fractions?
5. What are some strategies for combining fractions with different denominators?

**Tip:** Always simplify fractions as much as possible for the final answer to be in its simplest form.

Solve the fraction problem step-by-step: 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5. Learn how to multiply fractions, find the least common denominator, and combine terms. Perfect for students in Grades 6-8.

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