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The question asks for the fraction that is equivalent to the repeating decimal \( 0.\overline{5} \).

To express \( 0.\overline{5} \) (where 5 repeats) as a fraction, follow these steps:

1. Let \( x = 0.\overline{5} \). This means \( x = 0.55555\ldots \).
2. Multiply both sides by 10 to shift the decimal point:  
   \( 10x = 5.55555\ldots \).
3. Subtract the original equation from this new one:  
   \( 10x - x = 5.55555\ldots - 0.55555\ldots \),  
   which simplifies to \( 9x = 5 \).
4. Solve for \( x \) by dividing both sides by 9:  
   \( x = \frac{5}{9} \).

Thus, the fraction equivalent to \( 0.\overline{5} \) is \( \frac{5}{9} \).

Would you like further clarification or details?

Here are 5 related questions to explore:
1. How do you convert repeating decimals to fractions in general?
2. What is the decimal representation of \( \frac{7}{9} \)?
3. How would you handle converting \( 0.\overline{12} \) to a fraction?
4. Can all repeating decimals be converted to fractions?
5. What is the difference between terminating and repeating decimals?

**Tip**: For repeating decimals, always assign a variable to the decimal and use algebraic manipulation to eliminate the repeating part.

Learn how to convert the repeating decimal 0.5̅ into a fraction using algebraic manipulation. This step-by-step guide shows the process and explains the concept behind turning repeating decimals into fractions. Suitable for students in Grades 6-8.

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