Ta có : \(\dfrac{3}{8^{30}}< \dfrac{7}{8^{30}}\) ; \(\dfrac{7}{8^{40}}< 3\dfrac{8}{8^{40}}\)

\(\Rightarrow\dfrac{3}{8^{30}}+\dfrac{7}{8^{40}}< \dfrac{7}{8^{30}}+3\dfrac{8}{8^{40}}\)

Hay A<B

M=\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{17}{8^2.9^2}+\dfrac{19}{9^2.10^2}\)

=\(\dfrac{3}{1.4}+\dfrac{5}{4.9}+\dfrac{7}{9.16}+...+\dfrac{17}{64.81}+\dfrac{19}{81.100}\)

=\(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{64}-\dfrac{1}{81}+\dfrac{1}{81}-\dfrac{1}{100}\)

=1-\(\dfrac{1}{100}\)=\(\dfrac{99}{100}\)<\(\dfrac{100}{100}=1\)

.

Mình ko biết làm bạn ạ

`3/7-2/5`

`=1/35>0`

`=>3/7>2/5`

`b,9>8`

`=>1/9<1/8`

`=>5/9<5/8`

`d,8/7>1`

`7/8<1`

`=>8/7>7/8`

a) Ta có: \(\dfrac{3}{7}=\dfrac{15}{35}\)

\(\dfrac{2}{5}=\dfrac{14}{35}\)

Do đó: \(\dfrac{3}{7}>\dfrac{2}{5}\)

b) Ta có: 9>8

nên \(\dfrac{5}{9}< \dfrac{5}{8}\)

c) Ta có: \(\dfrac{8}{7}>1\)

\(1>\dfrac{7}{8}\)

Do đó: \(\dfrac{8}{7}>\dfrac{7}{8}\)

\(\dfrac{6}{7}+\dfrac{5}{8}=\dfrac{48}{56}+\dfrac{35}{56}=\dfrac{83}{56}\)

\(\dfrac{36}{12}-\dfrac{5}{3}=\dfrac{9}{3}-\dfrac{5}{3}=\dfrac{4}{3}\)

\(\dfrac{6}{7}+\dfrac{5}{8}=\dfrac{48}{56}+\dfrac{35}{56}=\dfrac{83}{56}\\\dfrac{36}{12}+\dfrac{5}{3}=\dfrac{36}{12}+\dfrac{20}{12} =\dfrac{56}{12}=\dfrac{14}{3}\)

6/7 + 5/8 = 48/56 + 35/56 = 83/56

36/12 - 5/3 = 36/12 - 20/12 = 16/12 = 4/3

2/

a/ \(\dfrac{7}{10}=\dfrac{7.15}{10.15}=\dfrac{105}{150}\)

\(\dfrac{11}{15}=\dfrac{11.10}{15.10}=\dfrac{110}{150}\)

-Vì \(\dfrac{105}{150}< \dfrac{110}{150}\)(105<110)nên \(\dfrac{7}{10}< \dfrac{11}{15}\)

b/ \(\dfrac{-1}{8}=\dfrac{-1.3}{8.3}=\dfrac{-3}{24}\)

-Vì \(\dfrac{-3}{24}>\dfrac{-5}{24}\left(-3>-5\right)\)nên\(\dfrac{-1}{8}>\dfrac{-5}{24}\)

c/\(\dfrac{25}{100}=\dfrac{25:25}{100:25}=\dfrac{1}{4}\)

\(\dfrac{10}{40}=\dfrac{10:10}{40:10}=\dfrac{1}{4}\)

-Vì \(\dfrac{1}{4}=\dfrac{1}{4}\)nên\(\dfrac{25}{100}=\dfrac{10}{40}\)

a/ \(\dfrac{7}{10}< \dfrac{11}{15}\)

c/ \(\dfrac{25}{100}=\dfrac{10}{40}\)

a) 

b) 

c) \(\dfrac{25}{100}=\dfrac{10}{40}\)

Câu 1 : 

\(\dfrac{-25}{37}\&\dfrac{-20}{31}\)

Ta thấy \(\dfrac{-25}{37}< \dfrac{-20}{37}\)

mà \(\dfrac{-20}{37}< \dfrac{-20}{31}\)

\(\Rightarrow\dfrac{-25}{37}< \dfrac{-20}{31}\)

Câu 2 :

\(\dfrac{2}{3}\&\dfrac{5}{7}\)

\(\dfrac{2}{3}:\dfrac{5}{7}=\dfrac{2}{3}.\dfrac{7}{5}=\dfrac{14}{15}< 1\)

Ta thấy \(\dfrac{8}{13}:\dfrac{5}{7}=\dfrac{8}{13}.\dfrac{7}{5}=\dfrac{56}{65}< 1\)

a) \(< \)

b) \(>\)

c) \(< \)

d) \(>\)

e) \(< \)

g) \(>\)

h) \(>\)

k) \(>\)

a)

b)

+) Quy đồng mẫu số ba phân số $\frac{1}{4};\frac{3}{4};\frac{5}{8}$

$\frac{1}{4} = \frac{{1 \times 2}}{{4 \times 2}} = \frac{2}{8}$

$\frac{3}{4} = \frac{{3 \times 2}}{{4 \times 2}} = \frac{6}{8}$ ; Giữ nguyên phân số $\frac{5}{8}$

Vì $\frac{2}{8} < \frac{5}{8} < \frac{6}{8}$ nên $\frac{1}{4} < \frac{5}{8} < \frac{3}{4}$

Vậy các phân số xếp theo thứ tự từ bé đến lớn là: $\frac{1}{4};\,\,\frac{5}{8};\,\,\frac{3}{4}$

+) Quy đồng mẫu số ba phân số $\frac{2}{3};\,\,\frac{2}{9};\,\,\frac{5}{9}$

$\frac{2}{3} = \frac{{2 \times 3}}{{3 \times 3}} = \frac{6}{9}$ ; Giữ nguyên phân số $\frac{2}{9}$; $\frac{5}{9}$

Vì $\frac{2}{9} < \frac{5}{9} < \frac{6}{9}$ nên $\frac{2}{9} < \frac{5}{9} < \frac{2}{3}$

Vậy các phân số xếp theo thứ tự từ bé đến lớn là $\frac{2}{9};\,\,\frac{5}{9};\,\,\frac{2}{3}$