To solve \(12 \frac{2}{5} - 17 \frac{1}{3}\), we first convert the mixed numbers into improper fractions.

1. Convert \(12 \frac{2}{5}\) to an improper fraction:
   \[
   12 \frac{2}{5} = \frac{12 \times 5 + 2}{5} = \frac{60 + 2}{5} = \frac{62}{5}
   \]

2. Convert \(17 \frac{1}{3}\) to an improper fraction:
   \[
   17 \frac{1}{3} = \frac{17 \times 3 + 1}{3} = \frac{51 + 1}{3} = \frac{52}{3}
   \]

Now subtract the fractions:
\[
\frac{62}{5} - \frac{52}{3}
\]

To subtract these, find a common denominator. The least common denominator (LCD) of 5 and 3 is 15.

- Rewrite \(\frac{62}{5}\) with denominator 15:
  \[
  \frac{62}{5} = \frac{62 \times 3}{5 \times 3} = \frac{186}{15}
  \]

- Rewrite \(\frac{52}{3}\) with denominator 15:
  \[
  \frac{52}{3} = \frac{52 \times 5}{3 \times 5} = \frac{260}{15}
  \]

Now subtract:
\[
\frac{186}{15} - \frac{260}{15} = \frac{186 - 260}{15} = \frac{-74}{15}
\]

So the result is:
\[
-\frac{74}{15}
\]

This can also be written as the mixed number:
\[
-\frac{74}{15} = -4 \frac{14}{15}
\]

Thus, the final answer is:
\[
-4 \frac{14}{15}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you convert mixed numbers into improper fractions?
2. What is the process of finding the least common denominator (LCD)?
3. How do you subtract fractions with unlike denominators?
4. Can you explain how to convert improper fractions back to mixed numbers?
5. What are some real-life applications of adding and subtracting mixed numbers?

**Tip**: When subtracting mixed numbers, always convert to improper fractions first for easier calculation.

This page provides a detailed step-by-step solution to the subtraction problem 12 2/5 - 17 1/3. It explains how to convert mixed numbers into improper fractions, find the least common denominator, and subtract fractions. This problem is suitable for students in Grades 5-7.

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