\(\left(\frac{3}{1.8}+\frac{3}{8.15}+\frac{3}{15.22}+...+\frac{3}{106.113}\right)-\left(\frac{25}{50.55}+\frac{25}{55.60}+...+\frac{25}{95.100}\right)\)
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F=(3/1.8+3/8.15+...+3/106.113)-(25/50.55+25/55.60+...+25/95.100) (1)
Đặt:
A=(3/1.8+3/8.15+3/15.22+...+3/106.113)
=3/7.(1-1/8+1/8-1/15+...+1/106-1/113)
=3/7.(1-1/113)
=3/7.112/113
=336/791. (2)
B=25/50.55+25/55.60+...+25/95.100
=25/5.(1/50-1/55+1/55-1/60+...+1/95-1/100)
=5.(1/50-1/100)
=1/20 (3)
Thay (2),(3) vào (1) ta được:
F=336/791-1/20
=5929/6720.
Tìm x :
x - 0,27 = \(\frac{73}{100}\)
x = \(\frac{73}{100}+0,27\)
x = 1
Cậu P khó quá mik chưa nghĩ ra cách tính nhanh nhất !
Cậu tự giải nhé !
Hok tốt
\(1\frac{13}{15}.0,75-\left(\frac{8}{15}+25\%\right).\frac{24}{47}-3\frac{12}{13}:3\)
\(=\frac{28}{15}.\frac{3}{4}-\left(\frac{8}{15}+\frac{1}{4}\right).\frac{24}{47}-\frac{51}{13}:3\)
\(=\frac{7}{5}-\frac{47}{60}.\frac{24}{47}-\frac{17}{13}\)
\(=\frac{7}{5}-\frac{2}{5}-\frac{17}{13}\)
\(=\frac{-4}{13}\)
\(4\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)\le x\le\frac{2}{3}.\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
\(\Leftrightarrow\frac{13}{3}.\frac{-1}{3}\le x\le\frac{2}{3}.\frac{-11}{12}\)
\(\Leftrightarrow\frac{-13}{9}\le x\le\frac{-11}{18}\)
\(\Leftrightarrow x=-1\)
\(8\frac{2}{7}-\left(1\frac{1}{6}+25\%\right)=\frac{58}{7}-\left(\frac{7}{6}+\frac{1}{4}\right)=\frac{58}{7}-\frac{17}{12}=\frac{577}{84}\)
\(4\frac{3}{4}+\left(-0,37\right)+\left(-1,28\right)+\left(-2,5\right)+3\frac{1}{12}\)
\(=\frac{19}{4}+\left(-\frac{83}{20}\right)+\frac{37}{12}=\frac{3}{5}+\frac{37}{12}=\frac{221}{60}\)
\(8\frac{2}{7}-\left(1\frac{1}{6}+25\%\right)=\frac{58}{7}-\left(\frac{7}{6}+\frac{1}{4}\right)=\frac{58}{7}-\frac{17}{12}=\frac{577}{84}\)
\(A=\frac{3}{1.8}+\frac{3}{8.15}+\frac{3}{15.22}+...+\frac{3}{106.113}\)
\(=\frac{3}{7}\left(\frac{7}{1.8}+\frac{7}{8.15}+\frac{7}{15.22}+...+\frac{7}{106.113}\right)\)
\(=\frac{3}{7}\left(\frac{8-1}{1.8}+\frac{15-8}{8.15}+\frac{22-15}{15.22}+...+\frac{113-106}{106.113}\right)\)
\(=\frac{3}{7}\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+\frac{1}{15}-\frac{1}{22}+\frac{1}{106}-\frac{1}{113}\right)\)
\(=\frac{3}{7}\left(1-\frac{1}{113}\right)=\frac{48}{113}\)
\(B=\frac{25}{50.55}+\frac{25}{55.60}+...+\frac{25}{95.100}\)
\(=5\left(\frac{5}{50.55}+\frac{5}{55.60}+...+\frac{5}{95.100}\right)\)
\(=5\left(\frac{55-50}{50.55}+\frac{60-55}{55.60}+...+\frac{100-95}{95.100}\right)\)
\(=5\left(\frac{1}{50}-\frac{1}{55}+\frac{1}{55}-\frac{1}{60}+...+\frac{1}{95}-\frac{1}{100}\right)\)
\(=5\left(\frac{1}{50}-\frac{1}{100}\right)=\frac{1}{20}\)
Giá trị của biểu thức đã cho là:
\(A-B=\frac{48}{113}-\frac{1}{20}=\frac{847}{2260}\)