Question

Find the difference.
9 2/3 - 2 1/9
Simplify your answer completely.
[__] [__]/[__]

Answer 1

To find the difference of \( 9 \frac{2}{3} - 2 \frac{1}{9} \), we first convert these mixed numbers into improper fractions.

1. **Convert \( 9 \frac{2}{3} \) to an improper fraction:**
\[
9 \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3}
\]

2. **Convert \( 2 \frac{1}{9} \) to an improper fraction:**
\[
2 \frac{1}{9} = \frac{2 \times 9 + 1}{9} = \frac{18 + 1}{9} = \frac{19}{9}
\]

3. **Now, subtract the two improper fractions:**
\[
\frac{29}{3} - \frac{19}{9}
\]

4. **Find a common denominator. The least common multiple of \( 3 \) and \( 9 \) is \( 9 \). We can convert \( \frac{29}{3} \) to a fraction with a denominator of \( 9 \):**
\[
\frac{29}{3} = \frac{29 \times 3}{3 \times 3} = \frac{87}{9}
\]

5. **Now we can subtract the fractions:**
\[
\frac{87}{9} - \frac{19}{9} = \frac{87 - 19}{9} = \frac{68}{9}
\]

6. **Now, we check if we can simplify \( \frac{68}{9} \).** Since \( 68 \) and \( 9 \) have no common factors (other than \( 1 \)), this fraction is already in its simplest form.

7. **Convert \( \frac{68}{9} \) back to a mixed number:**
- Divide \( 68 \) by \( 9 \):
\[
68 \div 9 = 7 \quad \text{(which is } 9 \times 7 = 63\text{)}
\]
- The remainder is:
\[
68 - 63 = 5
\]
- Therefore:
\[
\frac{68}{9} = 7 \frac{5}{9}
\]

The final answer for \( 9 \frac{2}{3} - 2 \frac{1}{9} \) is \( 7 \frac{5}{9} \).

So, in the requested format, the answer is:
\[
7 \quad 5 \quad 9
\]