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A,\(\frac{7}{13}+\frac{1}{7}+\frac{18}{30}=\frac{49}{91}+\frac{13}{91}+\frac{18}{30}=\frac{62}{91}+\frac{18}{30}=\frac{1860}{2730}+\frac{1638}{2730}=\frac{583}{455}\)
B,\(\left(\frac{20}{21}+\frac{3}{14}\right)-\frac{2}{3}=\left(\frac{280}{294}+\frac{63}{294}\right)-\frac{2}{3}=\frac{7}{6}-\frac{2}{3}=\frac{21}{18}-\frac{12}{18}=\frac{9}{18}=\frac{1}{2}\)
C,\(=\frac{17}{5}+\frac{31}{7}=\frac{119}{35}+\frac{155}{35}=\frac{234}{35}\)
\(\frac{11}{9}+\frac{35}{18}\)
\(=\frac{19}{6}\)
\(\frac{22}{21}:\frac{1}{2}+\frac{25}{12}:\frac{1}{2}\)
\(\frac{44}{21}+\frac{25}{6}\)
\(\frac{263}{42}\)
\(\left(1-\frac{1}{3}\right)\)\(x\left(1-\frac{1}{6}\right)\)\(x\)\(\left(1-\frac{1}{10}\right)\)\(x\)\(\left(1-\frac{1}{15}\right)\)\(x\)\(\left(1-\frac{1}{21}\right)\)\(x\)\(\left(1-\frac{1}{28}\right)\)\(=\)\(\left(\frac{3}{3}-\frac{1}{3}\right)\)\(x\)\(\left(\frac{6}{6}-\frac{1}{6}\right)\)\(x\)\(\left(\frac{10}{10}-\frac{1}{10}\right)\)\(x\)\(\left(\frac{15}{15}-\frac{1}{15}\right)\)\(x\)\(\left(\frac{21}{21}-\frac{1}{21}\right)\)\(x\)\(\left(\frac{28}{28}-\frac{1}{28}\right)\)\(=\)\(\frac{2}{3}x\frac{5}{6}x\frac{9}{10}x\frac{14}{15}x\frac{20}{21}x\frac{27}{28}\)\(=\)\(\frac{2x5x9x14x20x27}{3x6x10x15x21x28}\)\(=\)\(\frac{2x5\left(3x3\right)x\left(2x7\right)x\left(5x4\right)x\left(3x3x3\right)}{3x\left(3x2\right)x\left(5x2\right)x\left(5x3\right)x\left(7x3\right)x\left(4x7\right)}\)\(=\)\(\frac{3}{7}\)
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a \(\frac{4}{18}+\frac{5}{13}+\frac{7}{9}+\frac{21}{13}\)
= \(\left(\frac{4}{18}+\frac{7}{9}\right)+\left(\frac{5}{13}+\frac{21}{13}\right)\)
= \(1+2\)
= \(3\)
b \(\frac{4}{3}-\frac{2}{7}-\frac{5}{7}+\frac{2}{3}\)
= \(\left(\frac{4}{3}-\frac{2}{3}\right)-\left(\frac{2}{7}+\frac{5}{7}\right)\)
= \(\frac{2}{3}-1\)
= \(-\frac{1}{3}\)
\(P=\frac{1}{5x8}+\frac{1}{8x11}+.....+\frac{1}{602x605}\)
\(\Rightarrow3P=\frac{3}{5x8}+\frac{3}{8x11}+......+\frac{3}{602x605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-.....+\frac{1}{602}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{24}{121}\)
\(\Rightarrow P=\frac{24}{121}:3\)
\(\Rightarrow P=\frac{8}{121}\)