To solve \(-1 \frac{1}{4} - (-3 \frac{1}{6})\), follow these steps:

### Step 1: Convert mixed numbers to improper fractions.
- \( -1 \frac{1}{4} = -\frac{5}{4} \)
- \( -3 \frac{1}{6} = -\frac{19}{6} \)

### Step 2: Subtract the improper fractions.
We have:
\[
-\frac{5}{4} - (-\frac{19}{6}) = -\frac{5}{4} + \frac{19}{6}
\]
Now, find a common denominator for the fractions. The least common denominator (LCD) of 4 and 6 is 12.

### Step 3: Rewrite the fractions with the common denominator.
\[
-\frac{5}{4} = -\frac{15}{12}, \quad \frac{19}{6} = \frac{38}{12}
\]

### Step 4: Add the fractions.
\[
-\frac{15}{12} + \frac{38}{12} = \frac{23}{12}
\]

### Step 5: Convert back to a mixed number.
\[
\frac{23}{12} = 1 \frac{11}{12}
\]

Thus, the result is:
\[
1 \frac{11}{12}
\]

Would you like more details on any step or have any questions?

### Related questions:
1. How do you find the least common denominator between two numbers?
2. What is the process for converting improper fractions back to mixed numbers?
3. How do you add and subtract fractions with different denominators?
4. How do you simplify complex fractions with negative numbers?
5. What is the significance of mixed numbers in real-life applications?

### Tip:
When subtracting negative numbers, remember it becomes addition.

This guide demonstrates how to subtract mixed numbers like -1 1/4 - (-3 1/6) by converting them into improper fractions, finding the least common denominator, and solving step by step. Suitable for Grades 5-7 students learning fraction operations.

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