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To solve this problem, we need to maximize the result of the given expression:

\[
\frac{1}{\square} + \frac{1}{\square} = \frac{\square}{\square}
\]

We are given the four numbers 1, 2, 3, and 6, and each number can only be used once. The goal is to replace the boxes (denoted by "□") with these numbers in such a way that the result of the expression is maximized.

The expression consists of two fractions on the left-hand side, being added together, and the right-hand side is a fraction. To maximize the result, we need to carefully allocate the numbers to these fractions.

I'll try various combinations and evaluate the results. Let's proceed step-by-step.

We want to find the largest possible outcome. Let me compute the optimal allocation.The best arrangement of the numbers is as follows:

\[
\frac{1}{3} + \frac{1}{6} = \frac{1}{2}
\]

This gives:

\[
\frac{1}{3} + \frac{1}{6} = 0.5 \quad \text{and} \quad \frac{1}{2} = 0.5
\]

The left-hand side equals the right-hand side, making this the largest possible result with the numbers provided.

Would you like more details on this, or do you have any further questions?

Here are five related questions to explore:
1. How does changing the order of the numbers affect the result?
2. What is the smallest possible result using the same set of numbers?
3. Can you derive similar equations with different sets of numbers?
4. How does this approach change if the numbers were decimals?
5. What strategies work best when dealing with fractional sums and comparisons?

**Tip:** When solving problems involving fractions, it is often helpful to test extreme values first, as they tend to push results toward their maximum or minimum values.

If each of the four numbers 1, 2, 3, and 6 replaces a box in the fraction, what is the largest possible result of the expression, where each number can only be used once?

Solve the problem of maximizing a fraction expression using the numbers 1, 2, 3, and 6, where each number can only be used once. This problem explores basic fraction addition and simplification, perfect for students in Grades 6-8.

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