Solve the Fraction Addition: 2/6 + 1/4 + 2/12

To solve this problem, we will follow these steps:

• Step 1: Find the least common multiple (LCM) of the denominators.
• Step 2: Convert each fraction to an equivalent fraction with the common denominator.
• Step 3: Add the converted fractions.
• Step 4: Simplify the resulting fraction if possible.

Step 1: The denominators are 6, 4, and 12. The least common multiple of these numbers is 12.

Step 2: Convert each fraction to have the common denominator of 12.
- Convert $\frac{2}{6}$ to have the denominator 12: $\frac{2}{6} = \frac{4}{12}$ by multiplying numerator and denominator by 2.
- Convert $\frac{1}{4}$ to have the denominator 12: $\frac{1}{4} = \frac{3}{12}$ by multiplying numerator and denominator by 3.
- $\frac{2}{12}$ already has the denominator 12, so it remains unchanged: $\frac{2}{12}$.

Step 3: Add the numerators of the converted fractions:
$\frac{4}{12} + \frac{3}{12} + \frac{2}{12} = \frac{4 + 3 + 2}{12} = \frac{9}{12}$.

Step 4: Simplify the fraction if possible. Here, $\frac{9}{12}$ can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 3:
$\frac{9}{12} = \frac{3}{4}$.

Therefore, the solution to the problem is $\frac{9}{12}$.