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
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The Deep Dive
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!
