To solve the given expression, let's break down the steps:

**Step 1:** Simplify the given expression.  
The expression is:
\[
\left( \frac{7}{3} + \frac{4}{9} \right) \times \left( -\frac{1}{2} \right)^2
\]

**Step 2:** Add the fractions.
\[
\frac{7}{3} + \frac{4}{9}
\]

To add these fractions, we need a common denominator. The least common multiple of 3 and 9 is 9. Rewrite \(\frac{7}{3}\) with a denominator of 9:
\[
\frac{7}{3} = \frac{21}{9}
\]

Now add:
\[
\frac{21}{9} + \frac{4}{9} = \frac{25}{9}
\]

**Step 3:** Square \(-\frac{1}{2}\).
\[
\left( -\frac{1}{2} \right)^2 = \frac{1}{4}
\]

**Step 4:** Multiply \(\frac{25}{9}\) by \(\frac{1}{4}\).
\[
\frac{25}{9} \times \frac{1}{4} = \frac{25}{36}
\]

The final answer is:
\[
\frac{25}{36}
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you find a common denominator for adding fractions?
2. What is the process of squaring a negative fraction?
3. How do you multiply two fractions together?
4. Can fractions be simplified before performing arithmetic operations?
5. What are some real-life applications of fraction multiplication?

### Tip:
When squaring a fraction, remember that the square of a negative number is always positive.

Learn how to solve the fractional expression 7/3 + 4/9 multiplied by (-1/2) squared. This solution involves adding fractions, multiplying fractions, and using exponents. Suitable for students in Grades 6-8.

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