4. Sean paints \( \frac{7}{15} \) of a fence in one hour. He paints \( \frac{1}{10} \) of the fence less in the second hour. What fraction of the fence did Sean paint in two hours? Did he finish the job in two hours? no He painted

In the first hour, Sean paints \( \frac{7}{15} \) of the fence. In the second hour, he paints \( \frac{1}{10} \) of the fence less, which means he paints \( \frac{7}{15} - \frac{1}{10} \). To subtract these fractions, find a common denominator (which is 30), so it becomes \( \frac{14}{30} - \frac{3}{30} = \frac{11}{30} \). Adding both hours together gives us \( \frac{7}{15} + \frac{11}{30} = \frac{14}{30} + \frac{11}{30} = \frac{25}{30} = \frac{5}{6} \). Now, did Sean finish the job? He painted \( \frac{5}{6} \) of the fence in two hours, which means he did not finish the job, as \( \frac{1}{6} \) of the fence is left. It's important to remember that when working with fractions, finding a common denominator can make arithmetic easier. Always double-check your subtraction and addition when combining different fractions. Calculators can help avoid mistakes, but knowing how to do it manually is a valuable skill!