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\(A=2\dfrac{3}{13}\times\dfrac{13}{58}\times8\times2\dfrac{15}{24}\times\dfrac{8}{21}\)
\(A=\dfrac{29}{13}\times\dfrac{13}{58}\times8\times\dfrac{21}{8}\times\dfrac{8}{21}\)
\(A=\dfrac{29\times13\times8\times21\times8}{13\times58\times8\times21}\)
\(A=\dfrac{1\times1\times1\times1\times8}{1\times2\times1\times1}\)
\(A=\dfrac{8}{2}\)
\(A=4\)
\(A=\dfrac{29}{13}\cdot\dfrac{13}{58}\cdot8\cdot\dfrac{21}{8}\cdot\dfrac{8}{21}=\dfrac{1}{2}\cdot8=4\)
\(2\dfrac{3}{13}x\dfrac{27}{58}x2\dfrac{15}{24}x\dfrac{8}{21}:\dfrac{3}{7}\)
= \(\dfrac{29}{13}x\dfrac{27}{58}x\dfrac{63}{24}x\dfrac{8}{21}x\dfrac{7}{3}\)
= \(\dfrac{9x7}{13x2}=\dfrac{63}{26}\)
\(4\frac{5}{7}:1=\frac{33}{7}:1==\frac{33}{7}\)
\(\frac{5}{6}+2=\frac{5}{6}+\frac{12}{6}=\frac{17}{6}\)
\(\frac{7}{15}x\frac{21}{74}=\frac{7}{3x5}x\frac{3x7}{74}=\frac{7x7}{5x74}=\frac{49}{370}\)
So sánh phân số bằng cách nhanh nhất: a)2/15 và 8/17 b)12/17 và 13/18 c)9/20 và 3/7 d)17/18 và 15/19
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha