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Samantha likes to run at least 5 miles each day. She plans a new course: from home to the park is 1 1/3 miles, from the park to the library is 2 2/5 miles, and from the park to home is 2/3 mile. Will Samantha run at least 5 miles on this new course? Use only estimation to decide. Then explain if you are confident in your estimate or if you need to find an actual sum. Show your work.
[tex]\begin{gathered} 1\frac{1}{3}+2\frac{2}{5}+\frac{2}{3}=\frac{3+1}{3}+\frac{10+2}{5}+\frac{2}{3} \\ =\frac{4}{3}+\frac{12}{5}+\frac{2}{3} \\ =\frac{6}{3}+\frac{12}{5} \\ =2+\frac{12}{5} \\ =\frac{22}{5} \\ =4\frac{2}{5} \\ \\ \text{ thus samantha will NOT run at least 5 miles} \end{gathered}[/tex]
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