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\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}=-5\right)\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\right)=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-\frac{45}{2}=-5\)
\(\frac{3}{2}.x=\frac{35}{2}\)
\(x=\frac{35}{3}\)
\(=\frac{13\times10101}{15\times10101}+\frac{13\times10101}{35\times10101}+\frac{13\times10101}{63\times10101}+\frac{13\times10101}{99\times10101}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}=\frac{13}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{3}{7\times9}+\frac{2}{9\times11}\right)\)
\(=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{11}\right)=\frac{13}{2}\times\frac{8}{33}=\frac{52}{33}\)
\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{63.10101}\)+ \(\frac{13.10101}{99.10101}\)= \(\frac{13}{15}\) + \(\frac{13}{15}\) + \(\frac{13}{63}\)+ \(\frac{13}{99}\) =\(2\frac{82}{1155}\)
\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
=\(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
=\(13\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
=\(13.\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
=\(\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
=\(\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)
= \(\frac{13}{2}.\frac{8}{33}\)
=\(\frac{52}{33}\)
Rút gọn biểu thức S, ta có:
\(S=\frac{13}{30}+\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(\Leftrightarrow S=\frac{13}{30}+\left(\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{7\cdot9}+\frac{13}{9\cdot11}\right)\)
Đặt \(P=\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{7\cdot9}+\frac{13}{9\cdot11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+\frac{2}{9}-\frac{2}{11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3}-\frac{2}{11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{16}{33}\)
\(\Rightarrow P=\frac{104}{33}=3\frac{5}{33}\)
Ta có: \(P+1>P+\frac{13}{30}\)
Mà \(P+\frac{13}{30}=S\)
Còn \(P+1=3\frac{5}{33}+1=4\frac{5}{33}<5\)
\(\Rightarrow S<4\frac{5}{33}<5\)
Vậy đề bài sai.
Bài làm:
Ta có: \(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=\frac{13}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\frac{8}{33}=\frac{52}{33}\)
\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=13\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}\right)\)
\(=13\left[\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\right)\right]\)
\(=13\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{11}\right)\right]\)
\(=13\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\right]=13\cdot\frac{1}{2}\cdot\frac{8}{33}=\frac{52}{33}\)
A) \(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{10101\times13}{10101\times15}+\frac{10101\times13}{10101\times35}+\frac{10101\times13}{10101\times63}+\frac{10101\times13}{10101\times99}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\times\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=13\times\frac{4}{33}=\frac{52}{33}\)
B) \(\left(1998:18-1443:13\right)\times\left(16996-1110:30\times305\right)\)
\(=\left(111-111\right)\times\left(16996-1110:30\times305\right)\)
\(=0\times\left(16996-1110:30\times305\right)\)
\(=0\)
( TẤT CẢ MỌI SỐ NHÂN VỚI 0 ĐỀU BẰNG 0)
C) \(\left(\frac{575757}{424242}+\frac{575757}{565656}+\frac{575757}{727272}\right)\times18\)
\(=\left(\frac{10101\times57}{10101\times42}+\frac{10101\times57}{10101\times56}+\frac{10101\times57}{10101\times72}\right)\times8\)
\(=\left(\frac{57}{42}+\frac{57}{56}+\frac{57}{72}\right)\times8\)
\(=\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\times57\times8\)
\(=\frac{1}{169344}\times57\times8\)
\(=\frac{19}{7056}\)
MK KO BIẾT TÌNH NHANH ĐÂU! MK CHỈ LÀM ĐC NHƯ VẬY THÔI!!!!
CHÚC BN HỌC TỐT!!!!!!
a, = 13/15 + 13/35 + 13/63 + 13/99
= 13.( 1/15 + 1/35 + 1/63 + 1/99 )
= 13.( 1/ 3.5 + 1/5.7 + 1/7.9 + 1/ 9.11)
= 13 . ( 1/3 - 1/5 +1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11)
= 13 . ( 1/3 - 1/11)
= 13 . 3/11 = 39/11
\(\frac{3}{5}x-\frac{13}{9}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{13}{9}:13:\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\left(\frac{21}{315}+\frac{9}{315}+\frac{5}{315}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\frac{35}{315}=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\frac{1}{9}=-10\)
<=> \(\frac{3}{5}x-1=-10\)
<=> \(\frac{3}{5}x=-9\)
<=> \(x=-15\)
Vậy x = -15.
\(\frac{3}{5}x-1\frac{4}{9}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}\right)=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}=-10\right)\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{2}{3.5}+\frac{2}{.57}+\frac{2}{7.9}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{1}{3}-\frac{1}{9}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{2}.\frac{2}{9}\right)=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\frac{26}{18}=-10\)
\(\Leftrightarrow\frac{3}{5}x-1=-10\)
\(\Leftrightarrow\frac{3}{5}x=-10+1\)
\(\Leftrightarrow\frac{3}{5}x=-9\)
\(\Rightarrow x=-9:\frac{3}{5}\)
\(\Rightarrow x=-15\)
Vậy \(x=-15\)
\(a,\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{7.9}\right)\)
\(=13\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(=13.\frac{2}{9}=\frac{26}{9}\)
\(b,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}=\frac{2017}{2018}\)
P/s :Dấu chấm là dấu nhân nha
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