Let's break this down step by step:

We have the expression: $\frac{2}{3} - \frac{1}{4} + \left( -\frac{1}{2} \right) - \frac{1}{12}$

Step 1: Combine the fractions

To perform the operations, we'll first find a common denominator. The denominators are $3$, $4$, $2$, and $12$. The least common denominator (LCD) of $3$, $4$, $2$, and $12$ is $12$.

Step 2: Rewrite each fraction with the common denominator of 12

• $\frac{2}{3} = \frac{8}{12}$
• $\frac{1}{4} = \frac{3}{12}$
• $-\frac{1}{2} = \frac{-6}{12}$
• $\frac{1}{12}$ remains as $\frac{1}{12}$

Step 3: Substitute these values into the expression

Now the expression becomes: $\frac{8}{12} - \frac{3}{12} + \frac{-6}{12} - \frac{1}{12}$

Step 4: Perform the operations

Now, we combine the numerators: $8 - 3 - 6 - 1 = -2$

So, the result is: $\frac{-2}{12}$

Step 5: Simplify the fraction

$\frac{-2}{12} = \frac{-1}{6}$

Thus, the final answer is: $\boxed{-\frac{1}{6}}$

Do you want more details or have any questions?

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Here are 5 related questions for practice:

1. What is $\frac{5}{6} - \frac{2}{3} + \frac{1}{4} - \frac{1}{2}$?
2. Simplify $\frac{7}{8} - \frac{1}{3} + \frac{-3}{4} + \frac{5}{6}$.
3. How do you find the least common denominator (LCD) for fractions?
4. Solve $\frac{9}{12} - \frac{3}{8} + \frac{5}{16} - \frac{1}{4}$.
5. What is $\frac{3}{5} - \frac{1}{3} + \frac{2}{15}$?

Tip: Always look for the least common denominator when adding or subtracting fractions to simplify the process.