Let's re-evaluate the expression \(69 \frac{2}{9} - 31 \frac{1}{9} - 12 \frac{4}{9}\) and find the correct equivalent rational numbers.

1. Convert mixed numbers to improper fractions:
   \[
   69 \frac{2}{9} = \frac{69 \times 9 + 2}{9} = \frac{621 + 2}{9} = \frac{623}{9}
   \]
   \[
   31 \frac{1}{9} = \frac{31 \times 9 + 1}{9} = \frac{279 + 1}{9} = \frac{280}{9}
   \]
   \[
   12 \frac{4}{9} = \frac{12 \times 9 + 4}{9} = \frac{108 + 4}{9} = \frac{112}{9}
   \]

2. Perform the subtraction:
   \[
   69 \frac{2}{9} - 31 \frac{1}{9} - 12 \frac{4}{9} = \frac{623}{9} - \frac{280}{9} - \frac{112}{9}
   \]
   Combine the fractions:
   \[
   \frac{623 - 280 - 112}{9} = \frac{231}{9}
   \]

3. Simplify the improper fraction:
   \[
   \frac{231}{9} = 25 \frac{6}{9} = 25 \frac{2}{3}
   \]

Now, let's compare this result with the given options:

1. \(-26 \frac{5}{9}\)
2. \(\frac{239}{9}\)
3. \(50 \frac{5}{9}\)
4. \(\frac{455}{9}\)

We need to confirm the rational number equivalent to our result:

- \(\frac{231}{9}\) is an exact match to the simplified form we calculated.

However, if we re-check all given options:
- \( \frac{239}{9} \) and \(\frac{455}{9}\) are improper fractions not simplifying to our previous results.

The rational equivalents should be validated through direct calculation. Rechecking:

- Rational equivalent found previously was \( \frac{231}{9} = 25 \frac{6}{9} = 25 \frac{2}{3}\).

Thus, confirming proper validation, accurate matching \( \frac{231}{9} = 25 \frac{2}{3}\) equates rational equivalent form.

**Options accordingly**:
- \(\frac{239}{9}\)
- \(\frac{455}{9}\)
- 25 fractions (among given choices).

Correct confirmations imply:

1. \( -26 \frac{5}{9} \) Incorrect.
2. \( \frac{239}{9} \) Incorrect.
3. \( 50 \frac{5}{9} \) Incorrect.
4. \( \frac{455}{9} \) Incorrect.

Confirm correct rational form simplified alongside.

So, option: Confirm within **correct calculations** validating specific equivalent forms.

Would you like detailed options calculated? Adjust further mathematical queries listing:

1. Decimal to fractions conversions.
2. Mixed number improper fractional resolutions.
3. Simplified final fraction validation steps.
4. Mathematical rationalized steps ensuring.
5. Equivalent rational forms evaluated calculating.

**Tip:** Ensuring accurate mathematical fractional conversion validation confirming correct listed responses.

Learn how to solve the subtraction of mixed numbers and convert them to improper fractions step-by-step. This problem involves key concepts such as mixed numbers, improper fractions, and fraction simplification. Suitable for students in Grades 6-8.

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