Select all the correct answers.
Which rational number is equivalent to the expression 69 2/9 - 31 1/9 - (12 4/9)
? 
 -26 5/9
 239/9
 50 5/9
 455/9


To find the rational number equivalent to the expression \( 69 \frac{2}{9} - 31 \frac{1}{9} - 12 \frac{4}{9} \), we need to first convert the mixed numbers to improper fractions and then perform the subtraction.

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 to a mixed number:
   \[
   \frac{231}{9} = 25 \frac{6}{9} = 25 \frac{2}{3}
   \]

The equivalent rational number can also be represented as:
- \( 25 \frac{2}{3} \) or 
- \( \frac{231}{9} \)

Comparing this result to the provided options, we see:
- \(-26 \frac{5}{9}\) is incorrect.
- \(\frac{239}{9}\) is incorrect.
- \(50 \frac{5}{9}\) is incorrect.
- \(\frac{455}{9}\) is incorrect.

Thus, the expression simplifies to none of the provided options. However, there seems to be a mistake as there should be a correct answer within the given options. Re-evaluating, we see:

   \[
   69 \frac{2}{9} = \frac{69 \times 9 + 2}{9} = \frac{623}{9}
   \]
   \[
   31 \frac{1}{9} = \frac{31 \times 9 + 1}{9} = \frac{280}{9}
   \]
   \[
   12 \frac{4}{9} = \frac{12 \times 9 + 4}{9} = \frac{112}{9}
   \]
   \[
   69 \frac{2}{9} - 31 \frac{1}{9} - 12 \frac{4}{9} = \frac{623}{9} - \frac{280}{9} - \frac{112}{9}
   \]
   Combine the fractions:
   \[
   \frac{623 - 280 - 112}{9} = \frac{231}{9} = 25 \frac{6}{9} = 25 \frac{2}{3}
   \]

So the final rational equivalent of the expression given the closest match in provided choices is:

None of the provided options directly match, implying no correct options among the listed.

Would you like more details or have any questions? Here are 5 related questions you might ask:

1. How do you convert mixed numbers to improper fractions?
2. Can you explain the process of adding and subtracting fractions?
3. What are common errors to avoid when simplifying expressions with fractions?
4. How do you convert improper fractions back to mixed numbers?
5. What are rational numbers and how are they different from irrational numbers?

**Tip:** Always double-check each step of your calculation to ensure accuracy, especially when working with fractions.

Learn how to simplify the subtraction of mixed numbers: 69 2/9 - 31 1/9 - 12 4/9. Convert mixed numbers to improper fractions, perform subtraction, and simplify the result. Suitable for students in Grades 6-8.

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