Your friend says she used a common denominator to find fractions equivalent to $$ \frac{2}{3} $$ and $$ \frac{8}{9} $$, Is your friend orrect? Explain.

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To determine if your friend is correct in saying she used a common denominator to find fractions equivalent to $$ \frac{2}{3} $$ and $$ \frac{8}{9} $$, we need to analyze both fractions and see if they can be expressed with a common denominator.

1. **Identify the denominators**:
   - The denominator of $$ \frac{2}{3} $$ is $$ 3 $$.
   - The denominator of $$ \frac{8}{9} $$ is $$ 9 $$.

2. **Find the least common denominator (LCD)**:
   - The least common denominator of $$ 3 $$ and $$ 9 $$ is $$ 9 $$ because $$ 9 $$ is the smallest number that both $$ 3 $$ and $$ 9 $$ can divide into without leaving a remainder.

3. **Convert $$ \frac{2}{3} $$ to have the common denominator of $$ 9 $$**:
   - To convert $$ \frac{2}{3} $$ to a fraction with a denominator of $$ 9 $$, we can multiply both the numerator and the denominator by $$ 3 $$:
   $$
   \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
   $$

4. **Check $$ \frac{8}{9} $$**:
   - The fraction $$ \frac{8}{9} $$ already has the denominator of $$ 9 $$.

5. **Conclusion**:
   - Now we have:
     - $$ \frac{2}{3} = \frac{6}{9} $$
     - $$ \frac{8}{9} $$ remains as it is.
   - Both fractions can be expressed with the common denominator of $$ 9 $$.

Therefore, your friend is correct in saying she used a common denominator to find fractions equivalent to $$ \frac{2}{3} $$ and $$ \frac{8}{9} $$. The equivalent fractions are $$ \frac{6}{9} $$ for $$ \frac{2}{3} $$ and $$ \frac{8}{9} $$ remains the same.
Your friend is correct. By using a common denominator of 9, she converted $$ \frac{2}{3} $$ to $$ \frac{6}{9} $$ and kept $$ \frac{8}{9} $$ the same.

Your friend says she used a common denominator to find fractions equivalent to \( \frac{2}{3} \) and \( \frac{8}{9} \), Is your friend orrect? Explain.

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