Bài 1:

a) \(\frac{5^2.6^{11}.16^2+6^2.11^6.15^2}{2.6^{12}.10^{14}-81^2.960^3}=\frac{5^2.2^{19}.3^{11}+2^2.3^4.11^6.5^2}{2^{27}.3^{12}.5^{14}-3^{11}.2^{18}.5^3}\)

\(=\frac{5^2.2^2.3^4.\left(2^{17}.3^7+11^6\right)}{2^{18}.3^{11}.5^3.\left(2^9.3.5^{11}-1\right)}=\frac{2^{17}.3^7+11^6}{2^{16}.3^7.5.\left(2^9.3.5^{11}-1\right)}\)

b) Đặt A = 25²⁸ + 25²⁴ +....+ 25⁴ +1

=> 25⁴.A = 25³² + 25²⁸ +...+ 25⁸ + 25⁴

=> 25⁴.A - A = 25³² -1

\(A=\frac{25^{32}-1}{25^4-1}\)

tương tự....

Thay vào:

 \(\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}=\frac{\frac{25^{32}-1}{25^4-1}}{\frac{25^{32}-1}{25^2-1}}=\frac{25^2-1}{25^4-1}\)

bn làm kiểu g vậy mk ko hiểu

a) 

\(\frac{5}{6}=\frac{5X4}{6X4}=\frac{20}{24}\)

\(\frac{7}{8}=\frac{7X3}{8X3}=\frac{21}{24}\)

b)

\(\frac{22}{15}=\frac{22X5}{15X5}=\frac{110}{75}\)

\(\frac{17}{25}=\frac{17X3}{25X3}=\frac{51}{75}\)

đm mày

phân số có mẫu là `24` :

`-5/6=(-5xx4)/(6xx4)=-20/24`

`3/(-8) =-8/3=(-8xx8)/(3xx8)=-64/24`

`7/12=(7xx2)/(12xx2)=14/24`

`-25/100= -1/4= -6/24`

`72/108=2/3=16/24`

`10/60=1/6=4/24`

từ bé đến lớn là : `3/(-8) ; -5/6 ;-25/100; 10/60;72/108; 7/12`

-5/6=-20/24

-3/8=-9/24

7/12=14/24

-25/100=-1/4=-6/24

72/108=2/3=16/24

10/60=1/6=4/24

B

D

a) \(\dfrac{252525}{666666}=\dfrac{25.10101}{66.10101}=\dfrac{25}{66}\)

⇒\(\dfrac{25}{66}=\dfrac{252525}{666666}\)

b: \(\dfrac{23}{24}=1-\dfrac{1}{24}\)

\(\dfrac{24}{25}=1-\dfrac{1}{25}\)

mà \(-\dfrac{1}{24}>-\dfrac{1}{25}\)

nên \(\dfrac{23}{24}>\dfrac{24}{25}\)

a: \(\dfrac{25}{66}=\dfrac{252525}{666666}\)

b: \(\dfrac{23}{24}=1-\dfrac{1}{24}\)

\(\dfrac{24}{25}=1-\dfrac{1}{25}\)

mà \(-\dfrac{1}{24}< -\dfrac{1}{25}\)

nên \(\dfrac{23}{24}< \dfrac{24}{25}\)

18 : 40 = 0,45 = 45%

2,7 : 30 = 0,09 = 9%

24 : 60 = 0,4 = 40%

7,31 : 25 = 0,2924 = 29,24%

37,5 / 25 rút gọn là 3 / 2 nhé

37,5/25 BẠN NHÉ

Bài 1:

a: Cách 1: \(\frac37=\frac{3\cdot9}{7\cdot9}=\frac{27}{63};\frac59=\frac{5\cdot7}{9\cdot7}=\frac{35}{63}\)

mà 27<35

nên \(\frac37<\frac59\)

Cách 2: Ta có: \(\frac37=\frac{3\cdot5}{7\cdot5}=\frac{15}{35}\)

\(\frac59=\frac{5\cdot3}{9\cdot3}=\frac{15}{27}\)

mà \(\frac{15}{35}<\frac{15}{27}\left(35>27\right)\)

nên \(\frac37<\frac59\)

b: Cách 1: \(\frac{6}{12}=\frac{6\cdot3}{12\cdot3}=\frac{18}{36};\frac49=\frac{4\cdot4}{9\cdot4}=\frac{16}{36}\)

mà 18>16

nên \(\frac{6}{12}>\frac49\)

Cách 2: \(\frac{6}{12}=\frac{6\cdot2}{12\cdot2}=\frac{12}{24};\frac49=\frac{4\cdot3}{9\cdot3}=\frac{12}{27}\)

mà \(\frac{12}{24}>\frac{12}{27}\left(24<27\right)\)

nên \(\frac{6}{12}>\frac49\)

c: Cách 1: \(\frac{15}{25}=\frac{15\cdot18}{25\cdot18}=\frac{270}{450};\frac{54}{90}=\frac{54\cdot5}{90\cdot5}=\frac{270}{450}\)

Do đó: \(\frac{15}{25}=\frac{54}{90}\)

Cách 2: \(\frac{15}{25}=\frac{15:5}{25:5}=\frac35;\frac{54}{90}=\frac{54:18}{90:18}=\frac35\)

do đó: \(\frac{15}{25}=\frac{54}{90}\)

d: Cách 1: \(\frac{25}{30}=\frac{25\cdot3}{30\cdot3}=\frac{75}{90};\frac{75}{28}=\frac{75\cdot1}{28\cdot1}=\frac{75}{28}\)

mà \(\frac{75}{90}<\frac{75}{28}\left(90>28\right)\)

nên \(\frac{25}{30}<\frac{75}{28}\)

Cách 2: \(\frac{25}{30}=\frac{25\cdot14}{30\cdot14}=\frac{350}{420}\)

\(\frac{75}{28}=\frac{75\cdot15}{28\cdot15}=\frac{1125}{420}\)

mà 350<1125

nên \(\frac{25}{30}<\frac{75}{28}\)

e: cách 1: \(\frac{27}{45}=\frac{27\cdot4}{45\cdot4}=\frac{108}{180};\frac{18}{36}=\frac{18\cdot5}{36\cdot5}=\frac{90}{180}\)

mà 108>90

nên \(\frac{27}{45}>\frac{18}{36}\)

Cách 2: \(\frac{27}{45}=\frac{27\cdot2}{45\cdot2}=\frac{54}{90}\)

\(\frac{18}{36}=\frac{18\cdot3}{36\cdot3}=\frac{54}{108}\)

mà \(\frac{54}{90}>\frac{54}{108}\left(90<108\right)\)

nên \(\frac{27}{45}>\frac{18}{36}\)

là 30/25 vì 12/10 = 6/5 mà 6/5 lại bằng 30/25 nên 12/10=30/25

Phân số đó phải là 30/25 là đúng.