Divide \( 5 \frac{2}{3} \div 2 \frac{5}{9} \). Simplify the answer and write it as a mixed number, \( \frac{51}{23} \) \( \frac{23}{51} \) \( 2 \frac{391}{27} \) Submit

To solve \( 5 \frac{2}{3} \div 2 \frac{5}{9} \), first convert the mixed numbers to improper fractions: 1. For \( 5 \frac{2}{3} \): - \( 5 \times 3 + 2 = 15 + 2 = 17 \), so it becomes \( \frac{17}{3} \). 2. For \( 2 \frac{5}{9} \): - \( 2 \times 9 + 5 = 18 + 5 = 23 \), so it becomes \( \frac{23}{9} \). Now, dividing by a fraction is equivalent to multiplying by its reciprocal: \[ \frac{17}{3} \div \frac{23}{9} = \frac{17}{3} \times \frac{9}{23} = \frac{17 \times 9}{3 \times 23} = \frac{153}{69}. \] Now, simplify \( \frac{153}{69} \): Both the numerator and the denominator can be divided by 3: \[ \frac{153 \div 3}{69 \div 3} = \frac{51}{23}. \] This fraction is already in simplest form. But we need to express it as a mixed number: Since 51 divided by 23 is 2 (as 23 fits into 51 two times) with a remainder of 5, that gives us: \[ 2 \frac{5}{23}. \] So the final answer is \( 2 \frac{5}{23} \). It looks like we don't have that option directly available, but the correct calculation leads to \( \frac{51}{23} \) or \( 2 \frac{5}{23} \). You could submit \( \frac{51}{23} \) as a simplified answer and check if other options needed corrections. So, the correct answer among the options given should be checked for correctness: \( \frac{51}{23} \) is the final answer.