\(a,\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(=13\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{7.9}\right)\)

\(=13\left(\frac{1}{3}-\frac{1}{9}\right)\)

\(=13.\frac{2}{9}=\frac{26}{9}\)

\(b,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(=1-\frac{1}{2018}=\frac{2017}{2018}\)

P/s :Dấu chấm là dấu nhân nha

phần c đâu bn

\(=\frac{13\times10101}{15\times10101}+\frac{13\times10101}{35\times10101}+\frac{13\times10101}{63\times10101}+\frac{13\times10101}{99\times10101}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}=\frac{13}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{3}{7\times9}+\frac{2}{9\times11}\right)\)

\(=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{11}\right)=\frac{13}{2}\times\frac{8}{33}=\frac{52}{33}\)

\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{63.10101}\)+ \(\frac{13.10101}{99.10101}\)= \(\frac{13}{15}\) +   \(\frac{13}{15}\) + \(\frac{13}{63}\)+  \(\frac{13}{99}\) =\(2\frac{82}{1155}\)

\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

=\(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

=\(13\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)

=\(13.\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

=\(\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

=\(\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)

= \(\frac{13}{2}.\frac{8}{33}\)

=\(\frac{52}{33}\)

52/33

Bài làm:

Ta có: \(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(=\frac{13}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{13}{2}.\frac{8}{33}=\frac{52}{33}\)

\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(=13\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)

\(=13\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}\right)\)

\(=13\left[\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\right)\right]\)

\(=13\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{11}\right)\right]\)

\(=13\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\right]=13\cdot\frac{1}{2}\cdot\frac{8}{33}=\frac{52}{33}\)

Bài làm

\(X-70\frac{10}{11}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999990}\right)=5\)

\(X-70\frac{10}{11}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{131313}{999990}\right)=5\)

Chỗ này bạn đổi hỗn số ra số tự nhiên là 77. xg bạn tính trong ngoạc = bao nhiêu thì tính như bình thường, dễ lắm

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) \(\left(\frac{575757}{424242}+\frac{575757}{565656}+\frac{575757}{727272}\right)\times18\)

\(=\left(\frac{10101\times57}{10101\times42}+\frac{10101\times57}{10101\times56}+\frac{10101\times57}{10101\times72}\right)\times8\)

\(=\left(\frac{57}{42}+\frac{57}{56}+\frac{57}{72}\right)\times8\)

\(=\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\times57\times8\)

\(=\frac{1}{169344}\times57\times8\)

\(=\frac{19}{7056}\)

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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

5và 3/8-1 và 5/6