Subtract. Write your answer as a mixed number in simplest form. \( 5 \frac{4}{9}-4 \frac{1}{6} \)

To solve \( 5 \frac{4}{9}-4 \frac{1}{6} \), first, let's convert the mixed numbers into improper fractions. For \( 5 \frac{4}{9} \): \( 5 = \frac{5 \times 9}{1} = \frac{45}{9} \), so \( 5 \frac{4}{9} = \frac{45}{9} + \frac{4}{9} = \frac{49}{9} \). For \( 4 \frac{1}{6} \): \( 4 = \frac{4 \times 6}{1} = \frac{24}{6} \), so \( 4 \frac{1}{6} = \frac{24}{6} + \frac{1}{6} = \frac{25}{6} \). Now we need a common denominator to subtract these fractions. The least common multiple of 9 and 6 is 18. Convert \( \frac{49}{9} \) to an equivalent fraction with a denominator of 18: \( \frac{49}{9} \times \frac{2}{2} = \frac{98}{18} \). Convert \( \frac{25}{6} \) to an equivalent fraction with a denominator of 18: \( \frac{25}{6} \times \frac{3}{3} = \frac{75}{18} \). Now we can subtract: \[ \frac{98}{18} - \frac{75}{18} = \frac{98 - 75}{18} = \frac{23}{18}. \] Finally, to express \( \frac{23}{18} \) as a mixed number: Since \( 23 \div 18 = 1 \) remainder \( 5 \), we get: \[ 1 \frac{5}{18}. \] So, the answer is \( 1 \frac{5}{18} \).