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Answer:
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[tex]1. \: \(1 \frac{3}{2} + 1 \frac{3}{5} [/tex]
[tex]1 \frac{3}{2} = 1 + \frac{3}{2} = \frac{5}{2}\\
1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{8}{5}\\
\text{Convert to a common denominator:}\\
\frac{5}{2} = \frac{25}{10}\\
\frac{8}{5} = \frac{16}{10}\\
\frac{25}{10} + \frac{16}{10} = \frac{41}{10} = 4 \frac{1}{10} [/tex]
[tex]2. \: \(\frac{2}{11} + 2 \frac{1}{2} [/tex]
[tex]2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2}\\
\text{Convert to a common denominator:}\\
\frac{2}{11} + \frac{5}{2} = \frac{2 \cdot 2 + 5 \cdot 11}{2 \cdot 11} = \frac{4 + 55}{22} = \frac{59}{22} = 2 \frac{15}{22} [/tex]
[tex]3. \: \(1 \frac{1}{3} + \frac{1}{5}[/tex]
[tex]1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{4}{3}\\
\text{Convert to a common denominator:}\\
\frac{4}{3} + \frac{1}{5} = \frac{4 \cdot 5 + 1 \cdot 3}{3 \cdot 5} = \frac{20 + 3}{15} = \frac{23}{15} = 1 \frac{8}{15}[/tex]
[tex]4. \: \(2 \frac{3}{4} + \frac{2}{2}
[/tex]
[tex]2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{11}{4}\\
\frac{2}{2} = 1\\
\frac{11}{4} + 1 = \frac{11}{4} + \frac{4}{4} = \frac{15}{4} = 3 \frac{3}{4}[/tex]
[tex]5. \: \(1 \frac{1}{2} + \frac{2}{3}[/tex]
[tex]1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2}\\
\text{Convert to a common denominator:}\\
\frac{3}{2} + \frac{2}{3} = \frac{3 \cdot 3 + 2 \cdot 2}{2 \cdot 3} = \frac{9 + 4}{6} = \frac{13}{6} = 2 \frac{1}{6}[/tex]
[tex]6. \: \(3 \frac{1}{2} + \frac{4}{5}\)[/tex]
[tex]3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{7}{2}\\
\text{Convert to a common denominator:}\\
\frac{7}{2} + \frac{4}{5} = \frac{7 \cdot 5 + 4 \cdot 2}{2 \cdot 5} = \frac{35 + 8}{10} = \frac{43}{10} = 4 \frac{3}{10}[/tex]
[tex]7. \: \(4 \frac{1}{4} + 2 \frac{1}{6}\)[/tex]
[tex]4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{17}{4}\\
2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{13}{6}\\
\text{Convert to a common denominator:}\\
\frac{17}{4} + \frac{13}{6} = \frac{17 \cdot 3 + 13 \cdot 2}{4 \cdot 6} = \frac{51 + 26}{24} = \frac{77}{24} = 3 \frac{5}{24}
[/tex]
[tex]8. \: \( \frac{5}{6} + 3 \frac{3}{7} \)[/tex]
[tex]3 \frac{3}{7} = 3 + \frac{3}{7} = \frac{24}{7} \\
\text{Convert to a common denominator:} \\
\frac{5}{6} + \frac{24}{7} = \frac{5 \cdot 7 + 24 \cdot 6}{6 \cdot 7} = \frac{35 + 144}{42} = \frac{179}{42} = 4 \frac{11}{42}[/tex]
[tex]9. \: \( 5 \frac{2}{5} + 2 \frac{1}{4} \)[/tex]
[tex]5 \frac{2}{5} = 5 + \frac{2}{5} = \frac{27}{5} \\
2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{9}{4} \\
\text{Convert to a common denominator:} \\
\frac{27}{5} + \frac{9}{4} = \frac{27 \cdot 4 + 9 \cdot 5}{5 \cdot 4} = \frac{108 + 45}{20} = \frac{153}{20} = 7 \frac{13}{20}[/tex]
[tex]10. \: \( 20 \times 3 \frac{1}{9} + \frac{2}{3} \)[/tex]
[tex]3 \frac{1}{9} = 3 + \frac{1}{9} = \frac{28}{9} \\
\text{Multiply by 20:} \\
20 \times \frac{28}{9} = \frac{560}{9} \\
\text{Then add } \frac{2}{3}: \\
\frac{560}{9} + \frac{2}{3} = \frac{560 \cdot 3 + 2 \cdot 9}{9 \cdot 3} = \frac{1680 + 18}{27} = \frac{1698}{27} = 62 \frac{24}{27}[/tex]
[tex]1. \: \(1 \frac{3}{2} + 1 \frac{3}{5} = 4 \frac{1}{10}[/tex]
[tex]2. \: \(\frac{2}{11} + 2 \frac{1}{2} = 2 \frac{15}{22}[/tex]
[tex]3. \: \(1 \frac{1}{3} + \frac{1}{5} = 1 \frac{8}{15}[/tex]
[tex]4. \: \(2 \frac{3}{4} + \frac{2}{2} = 3 \frac{3}{4}[/tex]
[tex]5. \: \(1 \frac{1}{2} + \frac{2}{3} = 2 \frac{1}{6}[/tex]
[tex]6. \: \(3 \frac{1}{2} + \frac{4}{5} = 4 \frac{3}{10}[/tex]
[tex]7. \: \(4 \frac{1}{4} + 2 \frac{1}{6} = 3 \frac{5}{24}[/tex]
[tex]8. \: \( \frac{5}{6} + 3 \frac{3}{7} = 4 \frac{11}{42}[/tex]
[tex]9. \: \(5 \frac{2}{5} + 2 \frac{1}{4} = 7 \frac{13}{20}[/tex]
[tex]10. \: \(20 \times 3 \frac{1}{9} + \frac{2}{3} = 62 \frac{24}{27}[/tex]
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