To solve the problem of determining which model represents $\frac{1}{2} + \frac{1}{6}$, we will break it down:

Step 1: Find a common denominator.

• The denominators in $\frac{1}{2}$ and $\frac{1}{6}$ are 2 and 6, respectively.
• The least common denominator (LCD) is 6.

Step 2: Rewrite the fractions with the same denominator.

• $\frac{1}{2}$ can be rewritten as $\frac{3}{6}$ (since $\frac{1}{2} = \frac{3}{6}$).
• $\frac{1}{6}$ remains as $\frac{1}{6}$.

Step 3: Add the fractions.

• Now we can add $\frac{3}{6} + \frac{1}{6} = \frac{4}{6}$.
• Simplify $\frac{4}{6}$ to $\frac{2}{3}$.

Step 4: Analyze the models.

The correct model should represent $\frac{2}{3}$.

• A) Shows 4 out of 6 shaded, which represents $\frac{4}{6}$, or $\frac{2}{3}$. This is the correct model.
• B) Shows fewer parts shaded and doesn’t represent $\frac{1}{2} + \frac{1}{6}$.
• C) Shows more parts shaded, which would be incorrect for this sum.
• D) Shows $\frac{1}{2}$, but no additional shading for $\frac{1}{6}$.

Conclusion:

The correct answer is A).

Would you like more details or have any questions?

Here are 5 related questions to think about:

1. What is the least common denominator of $\frac{2}{5}$ and $\frac{3}{4}$?
2. How do you convert improper fractions to mixed numbers?
3. What visual model would represent $\frac{3}{4} + \frac{1}{2}$?
4. How do you subtract fractions with different denominators?
5. What is the visual difference between adding fractions and multiplying them?

Tip: Always simplify fractions after adding or subtracting to make calculations easier.