Answer :
Answer: The mixed number [tex]11\frac{5}{7}[/tex]
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Work Shown:
[tex]1\frac{2}{5} = 1+\frac{2}{5}\\\\3\frac{2}{7} = 3+\frac{2}{7}\\\\1\frac{2}{5}+3\frac{2}{7} = (1+\frac{2}{5}) + (3+\frac{2}{7})\\\\1\frac{2}{5}+3\frac{2}{7} = (1+3)+(\frac{2}{5}+\frac{2}{7})\\\\1\frac{2}{5}+3\frac{2}{7} = 4+(\frac{2*7}{5*7}+\frac{2*5}{7*5})\\\\1\frac{2}{5}+3\frac{2}{7} = 4+(\frac{14}{35}+\frac{10}{35})\\\\1\frac{2}{5}+3\frac{2}{7} = 4+\frac{14+10}{35}\\\\1\frac{2}{5}+3\frac{2}{7} = 4+\frac{24}{35}\\\\1\frac{2}{5}+3\frac{2}{7} = 4\frac{24}{35}\\\\[/tex]
Multiply that result by 2&1/2 to get...
[tex]4\frac{24}{35}*2\frac{1}{2} = (4+\frac{24}{35})*(2+\frac{1}{2})\\\\4\frac{24}{35}*2\frac{1}{2} = (4+\frac{24}{35})*\frac{5}{2}\\\\4\frac{24}{35}*2\frac{1}{2} = 4*\frac{5}{2}+\frac{24}{35}*\frac{5}{2}\\\\4\frac{24}{35}*2\frac{1}{2} = \frac{4*5}{2}+\frac{24*5}{35*2}\\\\4\frac{24}{35}*2\frac{1}{2} = 10+\frac{12}{7}\\\\4\frac{24}{35}*2\frac{1}{2} = 10+1+\frac{5}{7}\\\\4\frac{24}{35}*2\frac{1}{2} = 11+\frac{5}{7}\\\\4\frac{24}{35}*2\frac{1}{2} = 11\frac{5}{7}\\\\[/tex]