Áp dụng 1.5 ta có:
a) \(\dfrac{4}{9}< 1\Rightarrow\dfrac{4}{9}< \dfrac{4+9}{9+9}=\dfrac{13}{18}\).
b) \(\dfrac{-15}{7}< 1\Rightarrow\dfrac{-15}{7}< \dfrac{-15+3}{7+3}=\dfrac{-12}{10}=\dfrac{-6}{5}\).
c) \(\dfrac{278}{37}>1\Rightarrow\dfrac{278}{37}>\dfrac{278+9}{37+9}=\dfrac{278}{46}\).
d) \(\dfrac{-157}{623}< 1\Rightarrow\dfrac{-157}{623}< \dfrac{-157+16}{623+16}=\dfrac{-141}{639}=\dfrac{-47}{213}\);

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

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

\(\Rightarrow\)\(\dfrac{8}{18}\)>\(\dfrac{13}{18}\)

giữ nguyên \(\dfrac{13}{18}\) (vì \(8>13\))

- Vậy \(\dfrac{4}{9}>\dfrac{13}{18}\)

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

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

\(\Rightarrow\)\(-\dfrac{75}{35}< \dfrac{-42}{35}\)

\(-\dfrac{6}{5}=\dfrac{-6.7}{5.7}=\dfrac{-42}{35}\) (vì - 75>-42)

- vậy \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

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

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

\(\Rightarrow\)\(\dfrac{12788}{1702}>\dfrac{10286}{1702}\)

\(\dfrac{287}{46}=\dfrac{287.37}{46.37}=\dfrac{10286}{1702}\) (vì 12788>10286)

- vậy \(\dfrac{278}{37}>\dfrac{10286}{46}\)

d)\(-\dfrac{157}{623}\)và \(-\dfrac{47}{213}\)

\(-\dfrac{157}{623}=\dfrac{-157.213}{623.213}=\dfrac{-33441}{132699}\)

\(\Rightarrow\dfrac{-33441}{132699}< \dfrac{-29281}{132699}\)

\(\dfrac{-47}{213}=\dfrac{-47.623}{213.623}=\dfrac{-29281}{132699}\) (vì -33441<-29281)

-vậy \(-\dfrac{157}{623}< -\dfrac{47}{213}\)

a, Ta có : \(\dfrac{4}{9}=\dfrac{8}{18};\dfrac{13}{18}\)

Vì : 8< 13

mà 18 > 0 => \(\dfrac{8}{18}< \dfrac{13}{18}hay\dfrac{4}{9}< \dfrac{13}{18}\)

b,Ta có : \(\dfrac{-15}{7}=\dfrac{-75}{35}\);\(\dfrac{-6}{5}=\dfrac{-42}{35}\)

Vì -75 < -42 mà 35 > 0 => \(\dfrac{-75}{35}< \dfrac{-42}{35}\)

Hay \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

c,Ta có : \(\dfrac{278}{37}=\dfrac{12788}{1702}\);\(\dfrac{287}{46}=\dfrac{10619}{1702}\)

Vì 12788 > 10619 mà 1702 > 0

=> \(\dfrac{12788}{1702}>\dfrac{10619}{1702}Hay\dfrac{278}{37}>\dfrac{287}{46}\)

d,Ta có : \(\dfrac{-157}{623}=\dfrac{-33441}{132699};\dfrac{-47}{213}=\dfrac{-29281}{132699}\)

Vì -33441 < -29281 mà 132699 > 0

=> \(\dfrac{-33441}{132699}< \dfrac{-29281}{132699}Hay\dfrac{-157}{623}< \dfrac{-47}{213}\)

a, 4\9 < 13\18

b,-15\7 < -6\5

c,278\37 > 287\46

d,-157\623 < -47\213

a)<

b)<

c)>

d)<

a)     <

b)     <

c)     >

d)     <

1/Ta co :

\(\dfrac{15}{7}.\left(\dfrac{1}{5}-\dfrac{46}{45}\right)+\dfrac{46}{45}.\left(\dfrac{15}{7}-\dfrac{45}{46}\right)\)

=\(\dfrac{15}{7}.\dfrac{1}{5}-\dfrac{15}{7}.\dfrac{46}{45}+\dfrac{46}{45}.\dfrac{15}{7}-\dfrac{46}{45}.\dfrac{45}{46}\)

=\(\dfrac{15}{7}.\left(\dfrac{1}{5}-\dfrac{46}{45}+\dfrac{46}{45}\right)-1\)

=\(\dfrac{15}{7}.\dfrac{1}{5}-1\)

=\(\dfrac{3}{7}-1=\dfrac{-4}{7}\)

2/Ta co

\(\dfrac{43}{47}.\left(\dfrac{18}{37}+\dfrac{47}{43}\right)-\dfrac{18}{3}.\left(\dfrac{43}{47}+\dfrac{37}{36}\right)\)

=\(\dfrac{43}{47}.\dfrac{18}{37}+\dfrac{43}{47}.\dfrac{47}{43}-\dfrac{18}{37}.\dfrac{43}{47}+\dfrac{18}{37}.\dfrac{37}{36}\)

=\(\dfrac{18}{37}.\left(\dfrac{43}{37}-\dfrac{43}{37}+\dfrac{37}{36}\right)+1\)

=\(\dfrac{18}{37}.\dfrac{37}{36}+1\)

=\(\dfrac{1}{2}+1=\dfrac{3}{2}\)

tick cho mk nha

a) \(\dfrac{6}{14}=\dfrac{6:2}{14:2}=\dfrac{3}{7}\)

\(\dfrac{3}{7}< \dfrac{4}{7}\)

b) \(\dfrac{6}{15}=\dfrac{6:3}{15:3}=\dfrac{2}{5}\)

\(\dfrac{3}{5}>\dfrac{2}{5}\)

c) \(\dfrac{10}{18}=\dfrac{10:2}{18:2}=\dfrac{5}{9}\)

\(\dfrac{5}{9}>\dfrac{2}{9}\)

a. 7/9 - 16/9 = -9/9 = -1

b. 2/-15 + 7/10 = 17/30

c. (4 2/3 - 4 3/4) : -5/12 - 4/5 

= (14/3 - 19/4) : (-5/12) - 4/5

= -1/12 : (-5/12) - 4/5

= 1/5 - 4/5

= -3/5

\(a.\)

\(-\dfrac{2}{9}+\dfrac{7}{-9}=\dfrac{-2}{9}-\dfrac{7}{9}=\dfrac{-2-7}{9}=\dfrac{-9}{9}=-1\)

\(b.\)

\(\dfrac{1}{-6}+\dfrac{13}{-15}=-\dfrac{1}{6}-\dfrac{13}{15}=\dfrac{\left(-1\right)\cdot5-13\cdot2}{30}=\dfrac{-5-26}{30}=\dfrac{-31}{30}\)

\(c.\)

\(\dfrac{5}{-6}+\dfrac{-5}{12}+\dfrac{7}{18}=\dfrac{-5}{6}-\dfrac{5}{12}+\dfrac{7}{18}=\dfrac{\left(-5\right)\cdot6-5\cdot3+7\cdot2}{36}=\dfrac{-31}{36}\)

a) \(\dfrac{-2}{9}+\dfrac{7}{-9}=\dfrac{-2+-7}{9}=-1\) 

b)\(\dfrac{1}{-6}+\dfrac{13}{-15}=\dfrac{-5}{30}+\dfrac{26}{30}=\dfrac{-5+26}{30}=\dfrac{7}{10}\) 

c) \(\dfrac{5}{-6}+\dfrac{-5}{12}+\dfrac{7}{18}=\dfrac{-30}{36}+\dfrac{-15}{36}+\dfrac{18}{36}=\dfrac{-30+-15+18}{36}=\dfrac{-3}{4}\)

a) \(x=\dfrac{-2}{7}+\dfrac{9}{7}=1\) 

b) \(\dfrac{x}{3}=\dfrac{2}{5}+\dfrac{-4}{3}\) 

     \(\dfrac{x}{3}=\dfrac{-14}{15}\) 

\(\Rightarrow x=\dfrac{3.-14}{15}=\dfrac{-14}{5}\)

\(x=\dfrac{-2}{7}+\dfrac{9}{7}\) 

\(x=1\)

x=1

Trời ơi cái đề bài !!!

Thoy thì làm từng câu vậy

a) \(I=10101.\left(\dfrac{5}{111111}+\dfrac{5}{222222}-\dfrac{4}{111111}\right)\)

\(I=10101.\left(\dfrac{10}{222222}+\dfrac{5}{222222}-\dfrac{8}{222222}\right)\)

\(I=10101.\left(\dfrac{15}{222222}-\dfrac{8}{222222}\right)\)

\(I=10101.\dfrac{7}{222222}\)

\(I=\dfrac{7}{22}\)

1.

a) \(A=10101\left(\dfrac{5}{111111}+\dfrac{5}{222222}-\dfrac{4}{3.7.11.13.37}\right)\)\(A=\dfrac{10101.5}{10101.11}+\dfrac{10101.5}{10101.22}-\dfrac{10101.4}{10101.11}\)

\(A=\dfrac{5}{11}+\dfrac{5}{22}-\dfrac{4}{11}=\dfrac{7}{22}\)

\(B=\dfrac{2698}{45}-\left(\dfrac{344}{45}-\dfrac{17}{57}\right)\)

(Áp dụng tính chất a - (b - c) = a-b-c)

\(B=\dfrac{2698}{45}-\dfrac{344}{45}-\dfrac{17}{57}\)

\(B=\dfrac{2354}{45}-\dfrac{17}{57}\)

\(B=\dfrac{44726}{855}-\dfrac{255}{855}\)

\(B=\dfrac{44471}{855}\)