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a)\(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{23.27}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
b)\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
c)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{9.10}=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{3}-\frac{1}{13}+2\left(1-\frac{1}{10}\right)=\frac{10}{39}+\frac{9}{5}=\frac{401}{195}\)
\(\frac{5}{6}+\frac{7}{4}+\frac{11}{24}=\frac{20+42+11}{24}=\frac{73}{24}\)
\(\frac{5}{7}-\frac{2}{5}-\frac{3}{35}=\frac{25-14-3}{35}=\frac{8}{35}\)
\(\frac{4}{9}\times\frac{3}{2}\times\frac{9}{5}=\frac{4\times3\times9}{9\times2\times5}=\frac{6}{5}\)
\(\frac{21}{22}:\frac{7}{11}\times\frac{2}{3}=\frac{21}{22}\times\frac{11}{7}\times\frac{2}{3}=\frac{3}{2}\times\frac{2}{3}=1\)
Ta có:
\(A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)
\(A=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)
\(B=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\)
\(B=2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(B=2.\left(\frac{1}{1}-\frac{1}{10}\right)=2.\frac{9}{10}\)
\(B=\frac{9}{5}\)
a) ( 2/5 + 7/9 ) + 3/5
= ( 2/5 + 3/5 ) + 7/9
= 1 + 7/9
= 16/9
b) 3/4 + 2/7 + 1/4 + 3/5 + 5/7
= ( 3/4 + 1/4 ) + ( 2/7 + 5/7 ) + 1/4
= 1 + 1 + 1/4
= 9/4
c) 75/100 - 18/21 + 1/4 - 3/21
= 3/4 - 6/7 + 1/4 - 1/7
= ( 3/4 + 1/4 ) - ( 6/7 + 1/7 )
= 1 -1
= 0
d) 7/11 : 3/5 + 4/11 : 3/5
= ( 7/11 + 4/11 ) : 3/5
= 1 : 3/5
= 5/3
21/4 và 11/4 là hỗn số nhé giải nhanh cho mình với à cũng có cả cách làm nhé