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 \( 9 \frac{1}{4} \), we first convert both mixed numbers into improper fractions. Starting with \( 9 \frac{7}{9} \): \[ 9 \times 9 + 7 = 81 + 7 = 88 \] So, \( 9 \frac{7}{9} = \frac{88}{9} \). Now for \( 9 \frac{1}{4} \): \[ 9 \times 4 + 1 = 36 + 1 = 37 \] Thus, \( 9 \frac{1}{4} = \frac{37}{4} \). Now, we set up the division of the two improper fractions: \[ \frac{88}{9} \div \frac{37}{4} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{88}{9} \times \frac{4}{37} = \frac{88 \times 4}{9 \times 37} = \frac{352}{333} \] Next, we simplify \( \frac{352}{333} \). The numerator and denominator do not have any common factors, so it is already in its simplest form. Now, we convert this improper fraction back into a mixed number: To do this, divide 352 by 333: - 352 divided by 333 is 1 with a remainder of \( 352 - 333 = 19 \). Thus, we can express this as: \[ 1 \frac{19}{333} \] So, the final answer is: \[ 1 \frac{19}{333} \]