Solve: 2/3 + 1/4 + 5/6 + 1/12 Addition Problem

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

• Step 1: Determine the least common denominator (LCD) for all fractions.
• Step 2: Convert each fraction to have the LCD as the denominator.
• Step 3: Add the numerators of the fractions with the common denominator.
• Step 4: Simplify the resulting fraction if possible.

Now, let’s work through each step:

Step 1: The denominators are 3, 4, 6, and 12. The least common multiple of these numbers is 12. Thus, the LCD is 12.

Step 2: Convert each fraction:
- $\frac{2}{3}$ to an equivalent fraction with a denominator of 12:
Multiply both the numerator and denominator by 4 to get $\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$.
- $\frac{1}{4}$ to an equivalent fraction with a denominator of 12:
Multiply both the numerator and denominator by 3 to get $\frac{1 \times 3}{4 \times 3} = \frac{3}{12}$.
- $\frac{5}{6}$ to an equivalent fraction with a denominator of 12:
Multiply both the numerator and denominator by 2 to get $\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$.
- $\frac{1}{12}$ is already with the denominator 12, so it remains $\frac{1}{12}$.

Step 3: Add the numerators of these fractions:
$\frac{8}{12} + \frac{3}{12} + \frac{10}{12} + \frac{1}{12} = \frac{8 + 3 + 10 + 1}{12} = \frac{22}{12}$

Step 4: Simplify the fraction.
Since 22 and 12 share the common divisor 2, we simplify $\frac{22}{12}$ to $\frac{11}{6}$. This fraction cannot be simplified further.

Therefore, the solution to the problem is $\frac{11}{6}$.