\(\frac{13}{38}\)và  \(\frac{21}{64}\)

Vì \(\frac{13}{38}\)\(>\)\(\frac{13}{39}\)\(=\)\(\frac{1}{3}\)\(;\)\(\frac{1}{3}\)\(=\)\(\frac{21}{63}\)\(>\)\(\frac{21}{64}\)nên   \(\frac{13}{38}\)\(>\)\(\frac{21}{64}\).

13 x 64 = 832

38 x 21 = 798

Do đó: 13 x 64 > 38 x 21

=> 13 x 64 x 1/64 x 1/38 > 38 x 21 x 1/64 x 1/38

=> 13/38 > 21/64

Ta có : 

\(\frac{13}{38}>\frac{13}{39}\left(38< 39\right)\)

\(\Rightarrow\frac{13}{38}>\frac{1}{3}\left(1\right)\)

\(\frac{21}{64}< \frac{21}{63}\left(64>63\right)\)

\(\Rightarrow\frac{21}{64}< \frac{1}{3}\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\)

\(\Rightarrow\frac{21}{64}< \frac{1}{3}< \frac{13}{38}\)

\(\Rightarrow\frac{21}{64}< \frac{13}{38}\)

Vậy \(\frac{21}{64}< \frac{13}{38}\)

~ Ủng hộ nhé 

P/s :

Sử dụng phân số trung gian vào bài toán này : 

~ Ủng hộ nhé 

a) Ta so sánh \(\frac{214}{317}\)và \(\frac{21}{38}\)
Có \(\frac{21}{38}=\frac{189}{342}\)
Cũng có \(\frac{214}{317}+1=\frac{531}{317};\frac{189}{342}+1=\frac{531}{342}\)
=) \(\frac{531}{317}>\frac{531}{342}\)=) \(\frac{214}{317}+1>\frac{189}{342}+1\)=) \(\frac{214}{317}>\frac{189}{342}\)
=) \(\frac{214}{317}>\frac{21}{38}\)=) \(\frac{-214}{317}< \frac{-21}{38}\)
b) Có : \(\frac{-6}{17}=\frac{-12}{34};\frac{4}{-13}=\frac{-4}{13}=\frac{-12}{39}\)
=) \(\frac{-12}{34}< \frac{-12}{39}\)=) \(\frac{-6}{17}< \frac{4}{-13}\)

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

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 \(\frac{19}{15}>\frac{11}{15}\)

Ta dễ dàng nhận thấy: 26 < 64 và 38< 50 nên 26³⁸ < 64⁵⁰

Vậy 26³⁸ < 64⁵⁰            

So sánh 26³⁸ và 64⁵⁰

26³⁸=(2.13)³⁸=2³⁸.13³⁸

64⁵⁰=(2.32)⁵⁰=2⁵⁰.32⁵⁰

Vì 2³⁸ < 2⁵⁰ và 13³⁸ < 32⁵⁰

Nên 26³⁸ < 64⁵⁰