10. \( 4 \frac{2}{5}-1 \frac{5}{9}= \)

To solve \( 4 \frac{2}{5}-1 \frac{5}{9} \), first convert the mixed numbers into improper fractions. \( 4 \frac{2}{5} = \frac{22}{5} \) and \( 1 \frac{5}{9} = \frac{14}{9} \). Next, find a common denominator, which is 45. Convert the fractions: \( \frac{22}{5} = \frac{198}{45} \) and \( \frac{14}{9} = \frac{70}{45} \). Now, subtract the two: \( \frac{198}{45} - \frac{70}{45} = \frac{128}{45} \). Finally, convert back to a mixed number: \( 128 \div 45 = 2 \) remainder \( 38 \), so \( 2 \frac{38}{45} \) is your answer. Thus, \( 4 \frac{2}{5}-1 \frac{5}{9} = 2 \frac{38}{45} \). Quick tip: When working with mixed numbers, converting to improper fractions simplifies your calculations and makes it easier to manage fractions! And remember to always check your final answer for simplification. It's easy to overlook common factors!