To solve \((1 + \frac{1}{2})(1 - \frac{1}{2})\), we can apply the difference of squares formula:

\[
(a + b)(a - b) = a^2 - b^2
\]

Here, \( a = 1 \) and \( b = \frac{1}{2} \), so the expression becomes:

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

Now, calculate each term:

\[
1^2 = 1
\]
\[
\left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]

Thus, the expression simplifies to:

\[
1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}
\]

So, \((1 + \frac{1}{2})(1 - \frac{1}{2}) = \frac{3}{4}\).

Would you like any further details or explanations on this?

Here are 5 related questions you might find interesting:
1. What is the difference of squares formula?
2. How do you expand algebraic expressions like \((a + b)(a - b)\)?
3. Can you apply the difference of squares to \( (2 + 3)(2 - 3) \)?
4. How can we solve more complex fractions like \(\frac{1}{x}\)?
5. What is the significance of simplification in solving math problems?

**Tip:** The difference of squares formula is a useful shortcut when multiplying two binomials with opposite middle terms.

Learn how to solve the algebraic expression (1 + 1/2)(1 - 1/2) by applying the difference of squares formula. This step-by-step guide covers key concepts such as fractions and the difference of squares theorem. Suitable for students in Grades 7-8.

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