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: 

b) Ta có: 

c) Ta có: 

d) Ta có: 

e) Ta có: 

g) Ta có: 

a, \(\frac{6}{7}.\frac{16}{15}.\frac{7}{6}.\frac{21}{32}=\frac{6}{7}.\frac{7}{6}.\frac{16}{15}.\frac{21}{32}\)=\(1.\frac{16}{15}.\frac{21}{32}=\frac{7}{5.2}=\frac{7}{10}\)

Phần b T²

c,\(\frac{7}{4}.\frac{11}{21}+\frac{11}{21}.\frac{5}{4}=\frac{11}{21}.\left(\frac{7}{4}+\frac{5}{4}\right)\)=\(\frac{11}{21}.3=\frac{11}{7}\)

cảm ơn bạn nha

\(M=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{99}{100}\)

    \(=\frac{3.8.15.24....99}{4.9.16.25....100}\)

    \(=\frac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5....10.10}\)

     \(=\frac{1.2.3.4....9}{2.3.4.5....10}.\frac{3.4.5.6....11}{2.3.4.5....10}\)

    \(=\frac{1}{10}.\frac{11}{2}\)

     \(=\frac{11}{20}\)

Study well ! >_<

\(M=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{99}{100}\)

\(\Rightarrow M=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{9.11}{10.10}\)

\(\Rightarrow M=\frac{1.3.2.4.3.5...9.11}{2.2.3.3.4.4...10.10}\)

\(\Rightarrow M=\frac{\left(1.2.3...9\right)\left(3.4.5...11\right)}{\left(2.3.4...10\right)\left(2.3.4...10\right)}\)

\(\Rightarrow M=\frac{11}{10.2}\)

\(\Rightarrow M=\frac{11}{20}\)

\(M=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}...\cdot\frac{99}{100}\)

\(=\frac{3.8.15.24...99}{4.9.16.25....100}\)

\(=\frac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5....10.10}\)

\(=\frac{1.2.3....9}{2.3.4.5....10}\cdot\frac{3.4.5.6....11}{2.3.4.5....10}\)

\(=\frac{1}{10}\cdot\frac{11}{2}\)

\(=\frac{11}{20}\)

B = \(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{3599}{3600}\)

    = \(\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{59.61}{60.60}\)

    = \(\frac{2.4.3.5.4.6...59.61}{3.3.4.4.5.5...60.60}\)

    = \(\frac{2.3....59}{3.4...60}.\frac{4.5...61}{3.4...60}\)

    = \(\frac{2}{60}.\frac{61}{3}\)= \(\frac{61}{90}\)

Chúc bạn học tốt!

\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{899}{900}\)

\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{29.31}{30.30}\)

\(=\frac{\left(1\times2\times3\times...\times29\right)\left(3\times4\times5\times...\times31\right)}{\left(2\times3\times4\times...\times30\right)\left(2\times3\times4\times...\times30\right)}\)

\(=\frac{1\times2\times3\times...\times29}{2\times3\times4\times...\times30}.\frac{3\times4\times5\times...\times31}{2\times3\times4\times...\times30}\)

\(=\frac{1}{30}.\frac{31}{2}\)

\(=\frac{31}{60}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\\ =\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\\ =\frac{1.2.3.4....29}{2.3.4...30}.\frac{3.4.5...31}{2.3.4...30}\\ =\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

.

~ So sad :( !! ~

\(A=\frac{31}{60}\)

I thinks so ! Sad

Hình như sai đề bài bạn nhé! Đề bài đúng như dưới nhé!

\(\frac{3}{4}\).\(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}\)

= \(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.\frac{5.7}{6.6}.\frac{6.8}{7.7}\)

= \(\left(\frac{1.2.3.4.5.6}{2.3.4.5.6.7}\right).\left(\frac{3.4.5.6.7.8}{2.3.4.5.6.7}\right)\)

= \(\frac{1}{7}.\frac{8}{2}\)

= \(\frac{1}{7}.4=\frac{4}{7}\)

Hà ơi cho mình hỏi bạn lấy đề ở đâu vậy. Mình lấy đề ở trong sách NĂNG LỰC TỰ HỌC TOÁN 6 đấy.