Grade 5 math worksheet on dividing mixed numbers by mixed numbers, provided by K5 Learning.

To solve the problem of dividing mixed numbers by mixed numbers, we need to follow these steps:

1. Convert Mixed Numbers to Improper Fractions: A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. Place this result over the original denominator.

2. Divide the Improper Fractions: To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

3. Simplify the Result: If the result is an improper fraction, convert it back to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the new fraction, with the original denominator remaining the same.

Let's apply these steps to the first problem:

Problem 1: \(9 \frac{2}{3} \div 1 \frac{1}{3}\)

1. Convert Mixed Numbers to Improper Fractions:
- \(9 \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3}\)
- \(1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}\)

2. Divide the Improper Fractions:
- \(\frac{29}{3} \div \frac{4}{3} = \frac{29}{3} \times \frac{3}{4} = \frac{29 \times 3}{3 \times 4} = \frac{87}{12}\)

3. Simplify the Result:
- \(\frac{87}{12}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 87 and 12 is 3.
- \(\frac{87 \div 3}{12 \div 3} = \frac{29}{4}\)
- Convert \(\frac{29}{4}\) to a mixed number: \(29 \div 4 = 7\) with a remainder of 1, so \(\frac{29}{4} = 7 \frac{1}{4}\)

Therefore, the final answer for the first problem is:

Final Answer: \(7 \frac{1}{4}\)