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a) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}\)
\(=\dfrac{5}{7}\times\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)
\(=\dfrac{5}{7}\times1\)
\(=\dfrac{5}{7}\)
b) \(\dfrac{1}{10}+\dfrac{5}{9}+\dfrac{4}{9}+\dfrac{9}{10}-1\)
\(=\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\left(\dfrac{1}{10}+\dfrac{9}{10}-1\right)\)
\(=1+0\)
\(=1\)
c) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}+\dfrac{2}{7}\)
\(=\dfrac{5}{7}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{2}{7}\)
\(=\dfrac{5}{7}+\dfrac{2}{7}\)
\(=1\)
d) \(\dfrac{2}{7}+\dfrac{2}{8}+\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{4}{7}\)
\(=\left(\dfrac{2}{8}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{1}{7}+\dfrac{4}{7}\right)\)
\(=\left(\dfrac{1}{4}+\dfrac{1}{4}\right)+1\)
\(=\dfrac{1}{2}+1\)
\(=\dfrac{3}{2}\)
e) \(\dfrac{4}{5}+\dfrac{3}{10}+\dfrac{2}{10}+0,7\)
\(=\dfrac{4}{5}+\dfrac{5}{10}+\dfrac{7}{10}\)
\(=\dfrac{4}{5}+\dfrac{12}{10}\)
\(=\dfrac{4}{5}+\dfrac{6}{5}\)
\(=\dfrac{10}{5}\)
\(=2\)
g) \(362\times728+326\times272\)
\(=326\times\left(728+272\right)\)
\(=326\times1000\)
\(=326000\)
\(A=\frac{10}{5.7}+\frac{10}{7.9}+\frac{10}{9.11}+...+\frac{10}{33.35}\)
\(\Rightarrow A=10.\left(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{33.35}\right)\)
Đặt \(B=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{33.35}\)
\(\Rightarrow2B=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{33.35}\)
\(\Rightarrow2B=\frac{1}{5}-\frac{1}{35}=\frac{6}{35}\)
\(\Rightarrow B=\frac{3}{35}\)
\(\Rightarrow A=10.\frac{3}{35}=\frac{30}{35}=\frac{6}{7}\)
_Học tốt_
\(a.\frac{7}{5}+\frac{4}{7}-\frac{9}{10}=\frac{98}{70}+\frac{40}{70}-\frac{63}{70}=\frac{98+40-63}{70}=\frac{75}{70}\)\(=\frac{15}{14}\)
\(b.2+\frac{3}{4}x\frac{8}{5}=2+\frac{6}{5}=\frac{16}{5}\)
\(c.\frac{9}{8}-\frac{6}{5}:\frac{8}{5}=\frac{9}{8}-\frac{6}{5}x\frac{5}{8}=\frac{9}{8}-\frac{6}{8}=\frac{3}{8}\)
a)=(3/8+10/16)+(7/12+10/24)
=1+1=2
c)=(4/6+14/6)+(7/13+19/13)+(17/9+1/9)
=3+2+2=7
\(\frac{7}{5}+\frac{4}{7}-\frac{9}{10}=\frac{98}{70}+\frac{40}{70}-\frac{63}{70}=\frac{98+40-63}{70}=\frac{75}{70}=\frac{15}{14}\)
a)\(\frac{-3}{5}+\frac{1}{4}+\frac{-3}{10}\)
\(=\frac{-12}{20}+\frac{5}{20}+\frac{-6}{20}\)
\(=\frac{-13}{20}\)
b)\(\frac{1}{5}+\frac{-9}{10}+\frac{-7}{25}=\frac{10}{50}+\frac{-45}{50}+\frac{-14}{50}=\frac{-49}{50}\)
c)\(\frac{1}{5}+\frac{-1}{6}+\frac{1}{7}+\frac{-1}{8}+\frac{1}{9}+\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}+\frac{-1}{5}\)
=\(\left(\frac{1}{5}+\frac{-1}{5}\right)+\left(\frac{-1}{6}+\frac{1}{6}\right)+\left(\frac{1}{7}+\frac{-1}{7}\right)+\left(\frac{1}{8}+\frac{-1}{8}\right)+\frac{1}{9}\)
=\(0+0+0+0+\frac{1}{9}\)
=\(\frac{1}{9}\)
