a:Cách 1: \(\frac{21}{35}=\frac{21:7}{35:7}=\frac35\)

\(\frac{12}{40}=\frac{12:4}{40:4}=\frac{3}{10}\)

mà \(\frac35>\frac{3}{10}\left(5<10\right)\)

nên \(\frac{21}{35}>\frac{12}{40}\)

Cách 2: \(\frac{21}{35}=\frac{21\times8}{35\times8}=\frac{168}{280}\)

\(\frac{12}{40}=\frac{12\times7}{40\times7}=\frac{84}{280}\)

mà 168>84

nên \(\frac{21}{35}>\frac{12}{40}\)

b: Cách 1: \(\frac{35}{49}=\frac{35:7}{49:7}=\frac57\)

\(\frac{40}{64}=\frac{40:8}{64:8}=\frac58\)

mà \(\frac57>\frac58\left(7<8\right)\)

nên \(\frac{35}{49}>\frac{40}{64}\)

Cách 2: \(\frac{35}{49}=\frac{35\times64}{49\times64}=\frac{2240}{3136}\)

\(\frac{40}{64}=\frac{40\times49}{64\times49}=\frac{1960}{3136}\)

mà 2240>1960

nên \(\frac{35}{49}>\frac{40}{64}\)

c: Cách 1: \(\frac{9}{11}=1-\frac{2}{11}\)

\(\frac{13}{15}=1-\frac{2}{15}\)

Ta có: 11<15

=>\(\frac{2}{11}>\frac{2}{15}\)

=>\(-\frac{2}{11}<-\frac{2}{15}\)

=>\(-\frac{2}{11}+1<-\frac{2}{15}+1\)

=>\(\frac{9}{11}<\frac{13}{15}\)

Cách 2: Ta có: \(\frac{9}{11}=\frac{9\times15}{11\times15}=\frac{135}{165}\)

\(\frac{13}{15}=\frac{13\times11}{15\times11}=\frac{143}{165}\)

mà 135<143

nên \(\frac{9}{11}<\frac{13}{15}\)

d: Cách 1: \(\frac{21}{7}=\frac{21\times5}{7\times5}=\frac{105}{35}\)

mà 105>24

nên \(\frac{21}{7}>\frac{24}{35}\)

cách 2: Ta có: \(\frac{21}{7}=3>1;1>\frac{24}{35}\)

Do đó: \(\frac{21}{7}>\frac{24}{35}\)

e: Cách 1: \(\frac12=\frac{1\times2424}{2\times2424}=\frac{2424}{4848}\)

Cách 2: \(\frac{2424}{4848}=\frac{2424:2424}{4848:2424}=\frac12\)

f: Vì 19>11

nên \(\frac{19}{15}>\frac{11}{15}\)

a) Ta có: \(\dfrac{15}{7}>1\) (tử lớn hơn mẫu)

\(\dfrac{9}{14}< 1\) (tử nhỏ hơn mẫu)

Vậy: \(\dfrac{15}{7}>\dfrac{9}{14}\)

b) Ta có: 

\(\dfrac{899}{900}=1-\dfrac{1}{900}\)

\(\dfrac{1235}{1236}=1-\dfrac{1}{1236}\)

Mà: \(\dfrac{1}{900}>\dfrac{1}{1236}\)

Vậy: \(\dfrac{1235}{1236}>\dfrac{899}{900}\)

c) Ta có:

\(\dfrac{77}{75}=1+\dfrac{2}{75}\)

\(\dfrac{37}{35}=1+\dfrac{2}{35}\)

Mà: \(\dfrac{2}{75}< \dfrac{2}{35}\)

Vậy: \(\dfrac{37}{35}>\dfrac{77}{75}\)

\(\left\{{}\begin{matrix}\dfrac{15}{7}=\dfrac{30}{14}\\\dfrac{9}{14}< \dfrac{30}{14}\end{matrix}\right.\Rightarrow\dfrac{15}{7}>\dfrac{9}{14}\)

\(\left\{{}\begin{matrix}\dfrac{899}{900}=\dfrac{899.1236}{900.1236}=\dfrac{\text{1111164}}{900.1236}\\\dfrac{1235}{1236}=\dfrac{1235.900}{900.1236}=\dfrac{\text{1111500}}{900.1236}>\dfrac{\text{1111164}}{900.1236}\end{matrix}\right.\Rightarrow\dfrac{1235}{1236}>\dfrac{899}{900}\)

\(\left\{{}\begin{matrix}\dfrac{77}{75}=\dfrac{539}{525}\\\dfrac{37}{35}=\dfrac{555}{525}>\dfrac{539}{525}\end{matrix}\right.\Rightarrow\dfrac{77}{73}< \dfrac{37}{35}\)

a: 6^9=(6^3)^3=216^3>15^3

B: 6^36=(6^2)^18=36^18>35^18

c: 7^18=(7^2)^9=49^9>30^9

d: 3^500=243^100

7^300=343^100

=>3^500<7^300

a)=

b)>

c)=

a) 35 : 5 và (35 x 4) : (5 x 4)   

35:5= 7

(35 x 4) : (5 x 4) = 140 : 20 =7

=> 35 : 5  =  (35 x 4) : (5 x 4)            

b) 105 : 15 và (105 : 5) : (15 : 5)

105:15 =7

(105 : 5) : (15 : 5)= 7 : 3= 2 (dư 1)

=>105 : 15 > (105 : 5) : (15 : 5)

a)  − 1 5 + 4 − 5 = − 1 < 1 nên  − 1 5 + 4 − 5 < 1

b)  2 3 + − 1 5 = 7 15 ;   3 5 = 9 15 mà  7 15 < 9 15 nên  3 5 > 2 3 + − 1 5

21/35=3/5; 12/20=3/5

=>21/35=12/20

24/35<1<21/7

35/49=5/7; 40/64=5/8

=>35/49>40/64

2424/4848=1/2

9/11=1-2/11

13/15=1-2/15

mà 2/11>2/15

nên 9/11<13/15

19/15>11/15

khó

ko thì đi raaa

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