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.

Learn how to simplify the fraction expression 2/3 - 1/4 + (-1/2) - 1/12 with step-by-step instructions. This problem covers key fraction concepts such as finding the least common denominator (LCD), adding and subtracting fractions, and simplifying the result. Suitable for students in Grades 6-8.

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