Rút gọn phân số sau:\(\frac{\frac{2}{7}+\frac{2}{9}-\frac{2}{121}}{\frac{4}{7}+\frac{4}{9}-\frac{4}{121}}\)
Bài 1:Rút gọn
B = \(\frac{2}{3}-\frac{2}{5}-\frac{2}{7}-\frac{2}{9}\) / \(\frac{4}{3}-\frac{4}{5}-\frac{4}{7}-\frac{4}{9}\) ( Hai biểu thức này viết như phân số, cách nhau bằng đường kẻ, đoạn 2/3 ở trên, 4/3 ở dưới
Rút gọn A = \(\left(1-\frac{4}{1}\right)\left(1-\frac{4}{9}\right)\left(1-\frac{4}{25}\right)...\left(1-\frac{4}{121}\right)\)
A=-3.(1-(2/3)2)(1-(2/5)2)...(1-(2/11)2)=-3.(1-2/3)(1+2/3)(1-2/5)(1+2/5)...(1-2/11)(1+2/11)=-3.\(\frac{1}{3}\).\(\frac{5}{3}\).\(\frac{3}{5}\).\(\frac{7}{5}\)...\(\frac{9}{11}.\frac{13}{11}\)
= -\(\frac{13}{11}\)
Tính:
a) \(\frac{\frac{3}{5}+\frac{3}{27}-\frac{3}{9}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{27}-\frac{4}{9}-\frac{4}{11}}\)
b) \(\frac{5-\frac{5}{3}-\frac{5}{27}}{8-\frac{8}{3}-\frac{8}{27}}:\frac{15+\frac{15}{121}-\frac{15}{11}}{16+\frac{16}{121}-\frac{16}{11}}\)
c) \(\frac{1}{2}:\left(\frac{-3}{2}\right):\frac{4}{3}:\left(\frac{-5}{4}\right):\frac{6}{5}:\left(\frac{-7}{6}\right):...:\left(\frac{-101}{100}\right)\)
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Bài 1:Rút gọn các biểu thức sau:
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.....1\frac{1}{99}.1\frac{1}{120}-1\)
Bài 2:Tính:
a.A=\(\left(1+\frac{7}{9}\right).\left(1+\frac{7}{20}\right).\left(1+\frac{7}{33}\right).....\left(1+\frac{7}{153}\right).\left(1+\frac{7}{180}\right)\)
b.B=1+4+9+16+25+......+400
Bài 3:Cho dãy phân số:\(\frac{1}{1},\frac{1}{2},\frac{2}{1},\frac{1}{3},\frac{3}{1},\frac{1}{4},\frac{2}{3},\frac{3}{2},\frac{4}{1},..........\)
a.Viết 5 phân số tiếp theo của dãy
b.Hỏi phân số \(\frac{26}{7}\)là phân số thứ bao nhiêu của dãy?
\(\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}{\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)-\frac{1}{2}.\frac{1}{3}.\frac{1}{4}}\)+\(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{4}{9}-\frac{4}{7}-\frac{4}{11}}.\frac{1}{4}\)
Tính(rút gọn)
\(a,\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
\(b,5\cdot\frac{7}{5}\) \(c,\frac{1}{7}\cdot\frac{5}{9}+\frac{5}{9}\cdot\frac{1}{7}+\frac{5}{9}\cdot\frac{3}{7}\)
\(d,4\cdot11\cdot\frac{3}{4}\cdot\frac{9}{121}\)
\(e,\frac{3}{4}\cdot\frac{16}{9}-\frac{7}{5}:\frac{-21}{20}\)
\(g,2\frac{1}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\left(\frac{2}{3}+0,4\cdot5\right)\right]\)
a) Ta có: \(\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
\(=\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{9}{4}\cdot\frac{8}{3}\)
\(=4\cdot\frac{-1}{3}\cdot\frac{4}{7}\cdot3\)
\(=12\cdot\frac{-4}{21}=\frac{-48}{21}=\frac{-16}{7}\)
b) Ta có: \(5\cdot\frac{7}{5}=\frac{35}{5}=7\)
c) Ta có: \(\frac{1}{7}\cdot\frac{5}{9}+\frac{5}{9}\cdot\frac{1}{7}+\frac{5}{9}\cdot\frac{3}{7}\)
\(=\frac{5}{9}\left(\frac{1}{7}+\frac{1}{7}+\frac{3}{7}\right)\)
\(=\frac{5}{9}\cdot\frac{5}{7}=\frac{25}{63}\)
d) Ta có: \(4\cdot11\cdot\frac{3}{4}\cdot\frac{9}{121}\)
\(=\frac{4\cdot11\cdot3\cdot9}{4\cdot121}=\frac{27}{11}\)
e) Ta có: \(\frac{3}{4}\cdot\frac{16}{9}-\frac{7}{5}:\frac{-21}{20}\)
\(=\frac{4}{3}+\frac{4}{3}=\frac{8}{3}\)
g) Ta có: \(2\frac{1}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\left(\frac{2}{3}+0,4\cdot5\right)\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\frac{2}{3}+2\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\frac{7}{6}\)
\(=\frac{7}{3}-\frac{7}{18}=\frac{42}{18}-\frac{7}{18}=\frac{35}{18}\)
) Ta có: 1615⋅−514⋅5424⋅56211615⋅−514⋅5424⋅5621
=1615⋅−514⋅94⋅83=1615⋅−514⋅94⋅83
=4⋅−13⋅47⋅3=4⋅−13⋅47⋅3
=12⋅−421=−4821=−167=12⋅−421=−4821=−167
b) Ta có: 5⋅75=355=75⋅75=355=7
c) Ta có: 17⋅59+59⋅17+59⋅3717⋅59+59⋅17+59⋅37
=59(17+17+37)=59(17+17+37)
=59⋅57=2563=59⋅57=2563
d) Ta có: 4⋅11⋅34⋅91214⋅11⋅34⋅9121
=4⋅11⋅3⋅94⋅121=2711=4⋅11⋅3⋅94⋅121=2711
e) Ta có: 34⋅169−75:−212034⋅169−75:−2120
=43+43=83=43+43=83
g) Ta có: 213−13⋅[−32+(23+0,4⋅5)]213−13⋅[−32+(23+0,4⋅5)]
=73−13⋅[−32+23+2]=73−13⋅[−32+23+2]
=73−13⋅76=73−13⋅76
=73−718=4218−718=3518
Tính:
\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+.....+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}.\)
\(\frac{5-\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}+\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}.\)
rút gọn phân số sau:
A = \(\frac{1-\sqrt[1]{49}+\sqrt[1]{49}-\frac{1}{\left(7\sqrt{7}\right)^2}}{\sqrt{\frac{64}{2}}-\frac{4}{7}+\left(\frac{2}{7}\right)^2-\frac{4}{343}}\)
Viết phân số đảo ngược của các phân số sau :\(\frac{2}{3};\frac{4}{7};\frac{3}{5};\frac{9}{4};\frac{10}{7};\frac{5}{8};4;\frac{1}{2};\frac{3}{8};5;\frac{1}{3};\frac{1}{9}.\)
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