Lời giải:
a. $\frac{3}{-7}=\frac{-27}{63}$

$\frac{-5}{9}=\frac{-35}{63}$

Do $\frac{27}{63}< \frac{35}{63}$ nên $\frac{-27}{63}> \frac{-35}{63}$

$\Rightarrow \frac{3}{-7}> \frac{-5}{9}$

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b.

$-0,625=\frac{-625}{1000}=\frac{-5}{8}=\frac{-125}{200}$

$\frac{-19}{50}=\frac{-76}{200}> \frac{-125}{200}$

$\Rightarrow -0,625> \frac{-19}{50}$

c.

$-2\frac{5}{9}=-(2+\frac{5}{9})=\frac{-23}{9}=-(\frac{-23}{-9})$

a)      Ta có: \(\frac{2}{{ - 5}} = \frac{{ - 16}}{{40}}\) và \(\frac{{ - 3}}{8} = \frac{{ - 15}}{{40}}\)

Do \(\frac{{ - 16}}{{40}} < \frac{{ - 15}}{{40}}\,\, \Rightarrow \,\frac{2}{{ - 5}} < \frac{{ - 3}}{8}\).

b)      Ta có: \( - 0,85 = \frac{{ - 85}}{{100}} = \frac{{ - 17}}{{20}}\). Vậy \( - 0,85\)=\(\frac{{ - 17}}{{20}}\).

c)      Ta có: \(\frac{{37}}{{ - 25}} = \frac{{ - 296}}{{200}}\)  

Do  \(\frac{{ - 137}}{{200}} > \frac{{ - 296}}{{200}}\) nên \(\frac{{ - 137}}{{200}}\) > \(\frac{{37}}{{ - 25}}\) .

d)      Ta có: \( - 1\frac{3}{{10}}=\frac{-13}{10}\) ;

\(-\left( {\frac{{ - 13}}{{ - 10}}} \right) = \frac{{-13}}{{10}}\).

Vậy \(- 1\frac{3}{{10}} =-(\frac{{-13}}{{-10}})\,\).

Bài 1:

1)mik ko biết trục số ở đâu nên tham khảo:

2

-0,75 <5/3

\(-\frac{13}{15}+-\frac{2}{15}=-1;-\frac{14}{16}+-\frac{2}{16}\)

Vì \(-\frac{2}{15}< -\frac{2}{16}\Rightarrow\frac{-13}{15}< -\frac{14}{16}\)

2.Gọi 3 p/số đó là x;y;z

\(-\frac{5}{8}< x< y< z< -\frac{3}{5}\)

\(-\frac{100}{160}< x< y< z< -\frac{96}{160}\)

\(\Rightarrow x=-\frac{99}{160};y=-\frac{98}{160}=-\frac{49}{80};z=-\frac{97}{160}\)

Giải:

a) \(\dfrac{-3}{7}\) và \(\dfrac{2}{-5}\) 

\(\dfrac{-3}{7}=\dfrac{-3.5}{7.5}=\dfrac{-15}{35}\) 

\(\dfrac{2}{-5}=\dfrac{-2}{5}=\dfrac{-2.7}{5.7}=\dfrac{-14}{35}\) 

Vì \(\dfrac{-15}{35}< \dfrac{-14}{35}\) nên \(\dfrac{-3}{7}< \dfrac{2}{-5}\) 

b) \(\dfrac{-6}{7}\) và \(\dfrac{19}{23}\) 

Vì \(\dfrac{-6}{7}\) là số âm mà \(\dfrac{19}{23}\) là số dương nên \(\dfrac{-6}{7}< \dfrac{19}{23}\) 

c) \(\dfrac{-11}{23}\) và \(\dfrac{-13}{21}\) 

\(\dfrac{-11}{23}=\dfrac{-11.13}{23.13}=\dfrac{-143}{299}\) 

\(\dfrac{-13}{21}=\dfrac{-13.11}{21.11}=\dfrac{-143}{231}\) 

Vì \(\dfrac{-143}{299}>\dfrac{-143}{231}\) nên \(\dfrac{-11}{23}>\dfrac{-13}{21}\) 

d) \(\dfrac{-1}{5}\) và \(\dfrac{1}{100}\) 

Vì \(\dfrac{-1}{5}\) là số âm mà \(\dfrac{1}{100}\) là số dương nên \(\dfrac{-1}{5}< \dfrac{1}{100}\) 

Giải: (tiếp)

e) \(\dfrac{267}{-268}\) và \(\dfrac{-1347}{1343}\) 

\(\dfrac{267}{-268}=\dfrac{-267}{268}=\dfrac{-267.449}{268.449}=\dfrac{-119883}{120332}\) 

\(\dfrac{-1347}{1343}=\dfrac{-1347.89}{1343.89}=\dfrac{-119883}{119527}\)  

Vì \(\dfrac{-119883}{120332}>\dfrac{-119883}{119527}\) nên \(\dfrac{267}{-268}>\dfrac{-1347}{1343}\)

f) \(\dfrac{-13}{38}\) và \(\dfrac{29}{-88}\) 

\(\dfrac{-13}{38}=\dfrac{-13.29}{38.29}=\dfrac{-377}{1102}\)  

\(\dfrac{29}{-88}=\dfrac{-29}{88}=\dfrac{-29.13}{88.13}=\dfrac{-377}{1144}\) 

Vì \(\dfrac{-377}{1102}< \dfrac{-377}{1144}\) nên \(\dfrac{-13}{38}< \dfrac{29}{-88}\) 

g) \(\dfrac{4}{9}\) và \(\dfrac{13}{18}\) 

\(\dfrac{4}{9}=\dfrac{4.2}{9.2}=\dfrac{8}{18}\) 

Vì \(\dfrac{8}{18}< \dfrac{13}{18}\) nên \(\dfrac{4}{9}< \dfrac{13}{18}\) 

h) \(\dfrac{-15}{7}\) và \(\dfrac{-6}{5}\) 

\(\dfrac{-15}{7}=\dfrac{-15.5}{7.5}=\dfrac{-75}{35}\) 

\(\dfrac{-6}{5}=\dfrac{-6.7}{5.7}=\dfrac{-42}{35}\) 

Vì \(\dfrac{-75}{35}< \dfrac{-42}{35}\) nên \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

Giải:

i) \(\dfrac{278}{37}\) và \(\dfrac{287}{46}\) 

\(\dfrac{278}{37}=\dfrac{278.46}{37.46}=\dfrac{12788}{1702}\) 

\(\dfrac{287}{46}=\dfrac{287.37}{46.37}=\dfrac{10619}{1702}\) 

Vì \(\dfrac{12788}{1702}>\dfrac{10619}{1702}\) nên \(\dfrac{278}{37}>\dfrac{287}{46}\) 

k) \(\dfrac{4}{9}\) và \(\dfrac{16}{21}\) 

\(\dfrac{4}{9}=\dfrac{4.7}{9.7}=\dfrac{28}{63}\) 

\(\dfrac{16}{21}=\dfrac{16.3}{21.3}=\dfrac{48}{63}\) 

Vì \(\dfrac{28}{63}< \dfrac{48}{63}\) nên \(\dfrac{4}{9}< \dfrac{16}{21}\) 

l) \(\dfrac{-11}{5}\) và \(\dfrac{4}{13}\) 

Vì \(\dfrac{-11}{5}\) là số âm mà \(\dfrac{4}{13}\) là số dương nên \(\dfrac{-11}{5}< \dfrac{4}{13}\) 

m) \(\dfrac{36}{49}\) và \(\dfrac{23}{56}\) 

\(\dfrac{36}{49}=\dfrac{36.8}{49.8}=\dfrac{288}{392}\) 

\(\dfrac{23}{56}=\dfrac{23.7}{56.7}=\dfrac{161}{392}\) 

Vì \(\dfrac{288}{392}>\dfrac{161}{392}\) nên \(\dfrac{36}{49}>\dfrac{23}{56}\)

a)      +) Ta có: \( - 3,75 = \frac{{ - 375}}{{100}} = \frac{{ - 15}}{4} = \frac{{ - 45}}{{12}}\).

Do \( - 7 >  - 45\) nên \(\frac{{ - 7}}{{12}} > \frac{{ - 45}}{{12}}\).

+) Ta có: \(\frac{0}{{ - 3}} = 0\). Nên \(\frac{0}{{ - 3}} < \frac{4}{5}\).

b)      Các số hữu tỉ dương là: \(\frac{4}{5};\,5,12\).

Các số hữu tỉ âm là: \(\frac{{ - 7}}{{12}};\, - 3;\, - 3,75\)

Do \(\frac{0}{{ - 3}} = 0\) nên số không là số hữu tỉ dương cũng không là số hữu tỉ âm là: \(\frac{0}{{ - 3}}\).

câu 5 nhé

a)      Ta có \(\frac{{ - 2}}{3} < 0\) và \(\frac{1}{{200}} > 0\) nên \(\frac{{ - 2}}{3}\)<\(\frac{1}{{200}}\).

b)      Ta có: \(\frac{{139}}{{138}} > 1\) và \(\frac{{1375}}{{1376}} < 1\) nên \(\frac{{139}}{{138}}\) > \(\frac{{1375}}{{1376}}\).

c)      Ta có: \(\frac{{ - 11}}{{33}} = \frac{{ - 1}}{3}\) và \(\frac{{25}}{{ - 76}} = \frac{{ - 25}}{{76}} > \frac{{ - 25}}{{75}} = \frac{{ - 1}}{3}\,\,\,\, \Rightarrow \frac{{25}}{{ - 76}} > \frac{{ - 11}}{33}\).

a: -2/3<0<1/200

b: 139/138>1

1375/1376<1

=>139/138>1375/1376

c: -11/33=-1/3=-25/75<-25/76