Divide \( 9 \frac{7}{9} \) by \( 9 \frac{1}{4} \). Simplify the answer and write as a mixed number.

To divide \( 9 \frac{7}{9} \) by \( 9 \frac{1}{4} \) and express the result as a simplified mixed number, follow these steps: 1. **Convert Mixed Numbers to Improper Fractions:** - \( 9 \frac{7}{9} = \frac{9 \times 9 + 7}{9} = \frac{81 + 7}{9} = \frac{88}{9} \) - \( 9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{36 + 1}{4} = \frac{37}{4} \) 2. **Set Up the Division:** \[ \frac{88}{9} \div \frac{37}{4} = \frac{88}{9} \times \frac{4}{37} \] 3. **Multiply the Fractions:** \[ \frac{88 \times 4}{9 \times 37} = \frac{352}{333} \] 4. **Simplify the Fraction:** - Check for common factors between 352 and 333. Since 352 factors into \( 16 \times 22 \) and 333 factors into \( 3 \times 111 \), there are no common factors other than 1. - Therefore, \( \frac{352}{333} \) is already in its simplest form. 5. **Convert Back to a Mixed Number:** \[ \frac{352}{333} = 1 \frac{19}{333} \] (Because \( 352 \div 333 = 1 \) with a remainder of 19.) **Final Answer:** \[ 1 \frac{19}{333} \]