Let's solve the expression:

\[
\left(\frac{1}{3}\right)^2 - \left(\frac{1}{2}\right)^2
\]

1. Square each fraction:
\[
\left(\frac{1}{3}\right)^2 = \frac{1^2}{3^2} = \frac{1}{9}
\]
\[
\left(\frac{1}{2}\right)^2 = \frac{1^2}{2^2} = \frac{1}{4}
\]

2. Subtract the results:
\[
\frac{1}{9} - \frac{1}{4}
\]

To subtract these fractions, find a common denominator. The least common denominator (LCD) of 9 and 4 is 36.

\[
\frac{1}{9} = \frac{4}{36}, \quad \frac{1}{4} = \frac{9}{36}
\]

Now, subtract:
\[
\frac{4}{36} - \frac{9}{36} = \frac{4 - 9}{36} = \frac{-5}{36}
\]

Thus, the final answer is:
\[
\frac{-5}{36}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Simplify \(\left(\frac{2}{5}\right)^2 - \left(\frac{1}{4}\right)^2\).
2. What is the result of \(\left(\frac{1}{6}\right)^2 - \left(\frac{2}{3}\right)^2\)?
3. Find the value of \(\left(\frac{1}{3}\right)^2 + \left(\frac{1}{2}\right)^2\).
4. Simplify \(\left(\frac{3}{4}\right)^2 - \left(\frac{1}{3}\right)^2\).
5. Calculate \(\left(\frac{5}{6}\right)^2 - \left(\frac{1}{2}\right)^2\).

**Tip:** When subtracting fractions, always find the least common denominator before performing operations.

Explore the step-by-step solution for simplifying (1/3)² - (1/2)² using common denominators to subtract fractions. This problem covers key concepts in fractions and exponents, suitable for students in Grades 6-8.

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