1. The problem asks to convert the improper fraction $\frac{10}{3}$ to a mixed number and the mixed number $4 \frac{11}{12}$ to an improper fraction. 2. To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number part, and the remainder over the denominator is the fractional part. 3. For $\frac{10}{3}$, divide 10 by 3: $$10 \div 3 = 3 \text{ remainder } 1$$ So, the mixed number is: $$3 \frac{1}{3}$$ 4. To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. This sum becomes the new numerator over the original denominator. 5. For $4 \frac{11}{12}$: $$4 \times 12 + 11 = 48 + 11 = 59$$ So, the improper fraction is: $$\frac{59}{12}$$ 6. Final answers: - $\frac{10}{3} = 3 \frac{1}{3}$ - $4 \frac{11}{12} = \frac{59}{12}$