Giải đấy đủ giúp mình với 

a: =8/15x1/4=2/15

b: \(=\dfrac{5}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}=\dfrac{24}{21}=\dfrac{8}{7}\)

c: \(=\dfrac{2}{5}\left(\dfrac{3}{7}+\dfrac{4}{7}\right)=\dfrac{2}{5}\)

=3/2*4/3*5/4...*11/10

=5,5

a: \(=\dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{5}{6}=\dfrac{2}{3}\cdot\dfrac{2}{3}=\dfrac{4}{9}\)

b: \(=\dfrac{5}{6}\cdot\dfrac{1}{5}=\dfrac{1}{6}\)

a. C1: \(\dfrac{8}{15}.\dfrac{5}{6}=\dfrac{4}{9}\)

C2: \(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{5}{6}=\dfrac{2.4.5}{3.5.3.2}\)

Triệt tiêu phần giống nhau ở tử và mẫu ta có 

\(=\dfrac{4}{9}\)

b. \(C1:\left(\dfrac{1}{2}+\dfrac{1}{3}\right).\dfrac{1}{5}=\dfrac{5}{6}.\dfrac{1}{5}=\dfrac{1}{6}\)

C2: \(\dfrac{1}{2}.\dfrac{1}{5}+\dfrac{1}{3}.\dfrac{1}{5}=\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{1}{6}\)

Cách 1:

$(\frac{2}{3}\times \frac{4}{5})\times \frac{5}{6}=\frac{8}{15}\times \frac{5}{6}=\frac{8\times 5}{15\times 6}=\frac{2\times 2\times 2\times 5}{3\times 5\times 2\times 3}=\frac{4}{9}$

Cách 2:

$(\frac{2}{3}\times \frac{4}{5})\times \frac{5}{6}=\frac{2}{3}\times (\frac{4}{5}\times \frac{5}{6})=\frac{2}{3}\times \frac{4}{6}=\frac{2\times 4}{3\times 6}=\frac{2\times 4}{3\times 2\times 3}=\frac{4}{9}$

Cách 1:

$(\frac{1}{2}+\frac{}{}$

\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)

\(=\)\(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)

\(=\)\(\frac{9}{3}\)

\(=\)\(3\)

\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)

\(=\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)

Rút gọn phép tính trên ta được :

\(=\frac{9}{3}=3\)

A=1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+....+1(x+99)(x+100)A=1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+....+1(x+99)(x+100)

=1x−1x+1+1x+1−1x+2+1x+2−1x+3+....+1x+99−1x+ 100=1x-1x+1+1x+1-1x+2+1x+2-1x+3+....+1x+99-1x+ 100

=1x−1x+100=1x-1x+100

=x+100−xx(x+ 100)=x+100-xx(x+ 100)

=100x(x+100)

\(A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}\)

\(=\frac{3}{8}\)

Còn một câu hỏi nữa, làm sao để viết chữ phân số trong này thế?

812,5 nha

\(a,1\dfrac{4}{7}.3\dfrac{4}{11}.3\dfrac{11}{15}.5\dfrac{5}{8}\)

\(=\dfrac{11}{7}.\dfrac{27}{11}.\dfrac{56}{15}.\dfrac{45}{8}\)

\(=\dfrac{11.27.56.45}{7.11.15.8}\)

\(=\dfrac{1.3.7.3}{1.1.1.1}\)

\(=63\)

\(b,\dfrac{3}{4}.1\dfrac{1}{2}+\dfrac{3}{4}.\dfrac{1}{2}\)

\(=\dfrac{3}{4}.\left(1\dfrac{1}{2}+\dfrac{1}{2}\right)\)

\(=\dfrac{3}{4}.2\)

\(=\dfrac{3}{2}\)