Adding Fractions with Different Denominators: 1/3 and 1/6

To solve this problem, we'll follow these steps:

• Identify the common denominator.
• Convert each fraction to an equivalent fraction with the common denominator.
• Add the fractions.
• Verify the solution against given choices.

Now, let's work through each step:

Step 1: Identify the common denominator. For fractions $\frac{1}{3}$ and $\frac{1}{6}$, the least common multiple (LCM) of 3 and 6 is 6.

Step 2: Convert $\frac{1}{3}$ to have a denominator of 6. We do this by multiplying both the numerator and denominator by 2:

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

The fraction $\frac{1}{6}$ already has a denominator of 6, so we leave it unchanged:

$\frac{1}{6} = \frac{1}{6}$

Step 3: Add the fractions:

$\frac{2}{6} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6}$

The fraction $\frac{3}{6}$ simplifies to $\frac{1}{2}$, but since the task is to match with given choices, we note that there is no need to simplify further.

After comparing with the given choices, the option that matches our calculation is:

$\frac{3}{6}$