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\(a,\frac{0,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{13}}\)
\(=\frac{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}+\frac{3}{13}}{\frac{11}{4}-\frac{11}{5}+\frac{11}{7}+\frac{11}{13}}\)
\(=\frac{3\left[\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right]}{11\left[\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right]}=\frac{3}{11}\)
Câu b tương tự
#)Giải :
b)\(\frac{5}{9}:\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{9}:\left(\frac{1}{9}+\frac{2}{3}\right)\)
\(=\frac{5}{9}:\frac{1}{3}+\frac{5}{9}:\frac{1}{4}+\frac{5}{9}:\frac{1}{9}+\frac{5}{9}:\frac{2}{3}\)
\(=\frac{5}{9}:\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{9}+\frac{2}{3}\right)\)
\(=\frac{5}{9}:\frac{49}{36}\)
\(=\frac{20}{49}\)
\(\frac{\left(81,624:4\frac{4}{3}-4,505\right)+125\frac{3}{4}}{\left[\left(\left(\frac{11}{25}\right)^2:0,08+3,53\right)^2-\left(2,75\right)^2\right]:\frac{13}{25}}\)
\(=\frac{\left(\frac{10203}{125}.\frac{3}{16}-\frac{901}{200}\right)+\frac{503}{4}}{\left[\left(\frac{121}{625}.\frac{25}{2}+\frac{353}{100}\right)^2-\frac{121}{16}\right].\frac{25}{13}}\)
\(=\frac{\left(15,3045-\frac{901}{200}\right)+\frac{503}{4}}{\left(\frac{14161}{400}-\frac{121}{16}\right).\frac{25}{13}}\)
\(=\frac{136,5495}{\frac{696}{13}}\)
\(=2,550493534\)
a) \(2\frac{3}{4}\cdot\left(-0,4\right)-1\frac{3}{5}\cdot2,75+1,2:\frac{4}{11}\)
\(=2\frac{3}{4}\cdot\left(-\frac{2}{5}\right)-1\frac{3}{5}\cdot\frac{11}{4}+\frac{6}{5}:\frac{4}{11}\)
\(=\frac{11}{4}\cdot\left(-\frac{2}{5}\right)-1\frac{3}{5}\cdot\frac{11}{4}+\frac{6}{5}\cdot\frac{11}{4}\)
\(=\frac{11}{4}\left(-\frac{2}{5}-1\frac{3}{5}+\frac{6}{5}\right)\)
\(=\frac{11}{4}\left(-\frac{2}{5}-\frac{8}{5}+\frac{6}{5}\right)\)
\(=\frac{11}{4}\cdot\left(-\frac{4}{5}\right)=\frac{11}{1}\cdot\left(-\frac{1}{5}\right)=-\frac{11}{5}\)
b) \(\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)....\left(\frac{1}{31}+1\right)\)
\(=\left(\frac{1}{2}+\frac{2}{2}\right)\left(\frac{1}{3}+\frac{3}{3}\right)\left(\frac{1}{4}+\frac{4}{4}\right)...\left(\frac{1}{31}+\frac{31}{31}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{32}{31}\)
\(=\frac{3\cdot4\cdot5\cdot...\cdot32}{2\cdot3\cdot4\cdot...\cdot31}=\frac{32}{2}=16\)
c) Đặt \(C=1+2+3+...+30\)
Số số hạng là : \(\left(30-1\right):1+1=30\)(số)
Tổng của dãy số là : \(\frac{\left(1+30\right)\cdot30}{2}=465\)
Do đó : \(\frac{930}{C}=\frac{930}{465}=2\)
\(\frac{-1275}{100}-2,75:\left(\frac{-11}{4}.x+11\right)=\frac{-27}{2}\)
\(2,75:\left(\frac{-11}{4}.x+11\right)=\frac{-1275}{100}-\frac{-27}{2}\)
\(2,75:\left(\frac{-11}{4}.x+11\right)=\frac{-51}{4}-\frac{-54}{4}\)
\(2,75:\left(\frac{-11}{4}.x+11\right)=\frac{3}{4}\)
\(\frac{-11}{4}.x+11=2,75:\frac{3}{4}\)
\(\frac{-11}{4}.x+11=\frac{11}{4}:\frac{3}{4}\)
\(\frac{-11}{4}.x+11=\frac{11}{4}.\frac{4}{3}\)
\(\frac{-11}{4}.x+11=\frac{11}{3}\)
\(\frac{-11}{4}.x=\frac{11}{3}-11\)
\(\frac{-11}{4}.x=\frac{11}{3}-\frac{33}{3}\)
\(\frac{-11}{4}.x=\frac{-22}{3}\)
\(x=\frac{-22}{3}:\frac{-11}{4}\)
\(x=\frac{-22}{3}.\frac{4}{-11}\)
\(x=\frac{8}{3}\)
Vậy \(x=\frac{8}{3}\)