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The given mathematical expression is:

\[
\left[ \frac{3}{10} + \left( \frac{7}{4} - \frac{2}{5} \right) \right] - \frac{7}{20} \times \frac{4}{14}
\]

Let's break this down and solve it step-by-step:

### Step 1: Solve inside the parentheses
We first focus on the subtraction inside the parentheses: \( \frac{7}{4} - \frac{2}{5} \).

To subtract these fractions, we need a common denominator, which is 20. Rewriting the fractions with the common denominator:
\[
\frac{7}{4} = \frac{35}{20}, \quad \frac{2}{5} = \frac{8}{20}
\]
Now, perform the subtraction:
\[
\frac{35}{20} - \frac{8}{20} = \frac{27}{20}
\]

### Step 2: Add the result to \( \frac{3}{10} \)
Next, we add \( \frac{3}{10} \) to the result from Step 1. We again need a common denominator. The common denominator between 10 and 20 is 20. Rewriting \( \frac{3}{10} \):
\[
\frac{3}{10} = \frac{6}{20}
\]
Now, perform the addition:
\[
\frac{6}{20} + \frac{27}{20} = \frac{33}{20}
\]

### Step 3: Handle the multiplication \( \frac{7}{20} \times \frac{4}{14} \)
Perform the multiplication:
\[
\frac{7}{20} \times \frac{4}{14} = \frac{28}{280} = \frac{1}{10}
\]

### Step 4: Subtract the result from Step 3 from Step 2
Now subtract \( \frac{1}{10} \) from \( \frac{33}{20} \). First, rewrite \( \frac{1}{10} \) with a denominator of 20:
\[
\frac{1}{10} = \frac{2}{20}
\]
Now perform the subtraction:
\[
\frac{33}{20} - \frac{2}{20} = \frac{31}{20}
\]

### Final Answer:
The result of the expression is:
\[
\frac{31}{20}
\]

Would you like further clarification or a detailed explanation of any part of the solution?

Here are 5 related questions you might be interested in:
1. How do you add and subtract fractions with different denominators?
2. What is the process of multiplying fractions?
3. How can you simplify complex fractions after solving them?
4. What are common mistakes to avoid when working with fractions?
5. How can you convert improper fractions to mixed numbers?

**Tip**: Always check if the fractions can be simplified before performing operations to make calculations easier.

This step-by-step guide helps solve a math problem involving the addition, subtraction, and multiplication of fractions. It covers concepts of fraction operations and is suitable for students in Grades 6-8.

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