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The problem asks to evaluate the following expression:

\[
14 \frac{1}{6} - 10 \frac{11}{24}
\]

### Step 1: Convert the mixed numbers to improper fractions
For \( 14 \frac{1}{6} \):
\[
14 \frac{1}{6} = \frac{14 \times 6 + 1}{6} = \frac{84 + 1}{6} = \frac{85}{6}
\]

For \( 10 \frac{11}{24} \):
\[
10 \frac{11}{24} = \frac{10 \times 24 + 11}{24} = \frac{240 + 11}{24} = \frac{251}{24}
\]

### Step 2: Find a common denominator
The least common denominator of 6 and 24 is 24. Convert \(\frac{85}{6}\) to have a denominator of 24:

\[
\frac{85}{6} = \frac{85 \times 4}{6 \times 4} = \frac{340}{24}
\]

### Step 3: Subtract the fractions
Now, subtract \(\frac{251}{24}\) from \(\frac{340}{24}\):

\[
\frac{340}{24} - \frac{251}{24} = \frac{340 - 251}{24} = \frac{89}{24}
\]

### Step 4: Convert \(\frac{89}{24}\) to a mixed number
Divide 89 by 24:
\[
89 \div 24 \approx 3.71 \quad \text{(integer part is 3)}
\]
This means the mixed number is \( 3 \frac{17}{24} \).

### Final Answer
The result is:
\[
3 \frac{17}{24}
\]
Thus, the correct option is:

**B) 3 \(\frac{17}{24}\)**.

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

Here are 5 related questions for further practice:

1. Evaluate \( 12 \frac{3}{5} - 8 \frac{7}{10} \).
2. Simplify \( 5 \frac{7}{8} + 2 \frac{5}{12} \).
3. Convert \( 7 \frac{11}{15} \) into an improper fraction.
4. Subtract \( 9 \frac{2}{3} \) from \( 12 \frac{1}{4} \).
5. Find the least common multiple of 15 and 20.

**Tip:** Always check the denominators when adding or subtracting fractions, and find the least common denominator for simplicity.

Learn how to subtract mixed fractions such as 14 1/6 and 10 11/24. This step-by-step guide converts mixed numbers to improper fractions, finds the least common denominator, and provides the final result. Suitable for students in Grades 5-7.

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