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24 tháng 7 2017

a,

\(\dfrac{89}{-13}< 0< \dfrac{1}{123}\\ \Rightarrow\dfrac{89}{-13}< \dfrac{1}{123}\)

Vậy \(\dfrac{89}{-13}< \dfrac{1}{123}\)

b,

\(\dfrac{-13}{15}>\dfrac{-15}{15}=-1=\dfrac{-30}{30}>\dfrac{-31}{30}\)

Vậy \(\dfrac{-13}{15}>\dfrac{-31}{30}\)

c,

\(\dfrac{125}{123}=\dfrac{123}{123}+\dfrac{2}{123}=1+\dfrac{2}{123}\\ \dfrac{99}{97}=\dfrac{97}{97}+\dfrac{2}{97}=1+\dfrac{2}{97}\)

\(\dfrac{2}{97}>\dfrac{2}{123}\Rightarrow1+\dfrac{2}{97}>1+\dfrac{2}{123}\Leftrightarrow\dfrac{99}{97}>\dfrac{125}{123}\)

Vậy \(\dfrac{99}{97}>\dfrac{125}{123}\)

d,

\(\dfrac{125}{126}< \dfrac{126}{126}=1=\dfrac{986}{986}< \dfrac{987}{986}\)

Vậy \(\dfrac{125}{126}< \dfrac{987}{986}\)

22 tháng 7 2017

gianroi

a: \(A=\dfrac{-13}{21}=\dfrac{-26}{42}\)

\(B=\dfrac{-9}{14}=\dfrac{-27}{42}\)

mà -26>-27

nên A>B

b: \(A=\dfrac{99}{101}=1-\dfrac{2}{101}\)

\(B=\dfrac{2011}{2013}=1-\dfrac{2}{2013}\)

mà 2/101>2/2013

nên A<B

6 tháng 11 2024

 a;\(\dfrac{17}{24}\)  < \(\dfrac{17}{34}\) ⇒ \(\dfrac{-17}{24}\) > \(\dfrac{-17}{34}\) = - \(\dfrac{1}{2}\)

  \(\dfrac{25}{31}\)  > \(\dfrac{25}{50}\) ⇒ - \(\dfrac{25}{31}\)  < \(\dfrac{-25}{50}\) = - \(\dfrac{1}{2}\) 

    Vậy - \(\dfrac{17}{34}\) > - \(\dfrac{25}{31}\) 

6 tháng 11 2024

b;  \(\dfrac{27}{38}\) > \(\dfrac{27}{39}\) > \(\dfrac{25}{39}\) 

⇒ - \(\dfrac{27}{38}\) < - \(\dfrac{25}{39}\)  = \(\dfrac{-125}{195}\) 

Vậy - \(\dfrac{27}{38}\) < - \(\dfrac{125}{195}\)

 

10 tháng 8 2018

\(A=17\dfrac{2}{31}-\left(\dfrac{15}{17}+6\dfrac{2}{31}\right)=17\dfrac{2}{31}-\dfrac{15}{17}-6\dfrac{2}{31}\)

\(=11-\dfrac{15}{17}=\dfrac{172}{17}\)

\(B=\left(31\dfrac{6}{13}+5\dfrac{9}{41}\right)-36\dfrac{6}{12}=36\dfrac{363}{533}-36\dfrac{6}{12}=\dfrac{193}{1066}\)

\(C=27\dfrac{51}{59}-\left(7\dfrac{51}{59}-\dfrac{1}{3}\right)=27\dfrac{51}{59}-7\dfrac{51}{59}+\dfrac{1}{3}=20+\dfrac{1}{3}=\dfrac{61}{3}\)

10 tháng 8 2018

\(A=17\dfrac{2}{31}-\left(\dfrac{15}{17}+6\dfrac{2}{31}\right)=17\dfrac{2}{31}-\dfrac{15}{17}-6\dfrac{2}{31}\)

\(=\left(17\dfrac{2}{31}-6\dfrac{2}{31}\right)-\dfrac{15}{17}=11-\dfrac{15}{17}=\dfrac{172}{17}\)

\(B=\left(31\dfrac{6}{13}+5\dfrac{9}{41}\right)-36\dfrac{6}{12}=36\dfrac{363}{533}-36\dfrac{1}{2}=\dfrac{193}{1066}\) (Casio :>)

\(C=27\dfrac{51}{59}-\left(7\dfrac{51}{59}-\dfrac{1}{3}\right)=27\dfrac{51}{59}-7\dfrac{51}{59}+\dfrac{1}{3}\)

\(=20+\dfrac{1}{3}=\dfrac{61}{3}\)

AH
Akai Haruma
Giáo viên
23 tháng 9 2018

Lời giải:
\(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk, c=dk \)

Khi đó:

\(\frac{2002a+2003b}{2002a-2003b}=\frac{2002bk+2003b}{2002bk-2003b}=\frac{b(2002k+2003)}{b(2002k-2003)}=\frac{2002k+2003}{2002k-2003}(1)\)

\(\frac{2002c+2003d}{2002c-2003d}=\frac{2002dk+2002d}{2002dk-2003d}=\frac{d(2002k+2003)}{d(2002k-2003)}=\frac{2002k+2003}{2002k-2003}(2)\)

Từ \((1);(2)\Rightarrow \frac{2002a+2003b}{2002a-2003b}=\frac{2002c+2003d}{2002c-2003d}\)

Ta có đpcm.

23 tháng 9 2018

Xét tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\) . Gọi giá trị chung của các tỉ số đó là k, ta có:

\(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=> \(a=k.b,c=k.d\)

Ta có :

( 1 )

= \(\dfrac{2002a+2003b}{2002a-2003b}=\dfrac{2002kb+2003b}{2002kb-2003b}\)

= \(\dfrac{b.\left(2002k+2003\right)}{b.\left(2002k-2003\right)}=\dfrac{2002k+2003}{2002k-2003}\)

( 2 ) \(\dfrac{2002c+2003d}{2002c-2003d}=\dfrac{2002kd+2003d}{2002kd-2003d}\)

= \(\dfrac{d.\left(2002k+2003\right)}{d.\left(2002k-2003\right)}=\dfrac{2002k+2003}{2002k-2003}\)

Từ ( 1 ) và ( 2 ) => \(\dfrac{2002a+2003b}{2002a-2003b}=\dfrac{2002c+2003d}{2002c-2003d}\)

17 tháng 6 2017

a,\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(-\dfrac{3}{5}+\dfrac{3}{5}\right)+.....+\left(-\dfrac{11}{13}+\dfrac{11}{13}\right)+\dfrac{13}{15}\)

\(=0+0+...0+0+\dfrac{13}{15}=\dfrac{13}{15}\)

câu b và c xem lại đề nha

Chúc bạn học tốt!!!

17 tháng 6 2017

Đề đúng mà bạn

1 tháng 8 2017

a) \(\dfrac{12}{47}\)\(\dfrac{11}{53}\)

Ta có: \(\dfrac{11}{47}>\dfrac{11}{53}\)\(\dfrac{12}{47}>\dfrac{11}{47}\)

\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)

1 tháng 8 2017

a) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{11}{44}>\dfrac{11}{53}\)

\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)

b) Ta có : \(\dfrac{456}{461}=1-\dfrac{5}{461}\)

\(\dfrac{123}{128}=1-\dfrac{5}{128}\)

\(\dfrac{5}{461}< \dfrac{5}{128}\Rightarrow1-\dfrac{5}{461}>1-\dfrac{5}{128}\)

\(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\)

c) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{19}{76}>\dfrac{19}{77}\)

=> \(\dfrac{12}{47}>\dfrac{19}{77}\)

d) Ta có : \(13A=13.\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{16}+13}{13^{16}+1}=\dfrac{13^{16}+1+12}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)

\(13B=13.\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)

Ta thấy : \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\Rightarrow\dfrac{13^{15}+1}{13^{16}+1}>\dfrac{13^{16}+1}{13^{17}+1}\)

Bài 1: 

a: \(=17+\dfrac{2}{31}-\dfrac{15}{17}-6-\dfrac{2}{31}=11-\dfrac{15}{17}=\dfrac{172}{17}\)

b: \(=31+\dfrac{6}{13}+5+\dfrac{9}{41}-36-\dfrac{9}{41}-36-\dfrac{6}{13}\)

=36

c: \(=27+\dfrac{51}{59}-7-\dfrac{51}{59}+\dfrac{1}{3}=20+\dfrac{1}{3}=\dfrac{61}{3}\)

10 tháng 7 2017

1. Tìm n, biết:

a) \(\dfrac{-32}{\left(-2\right)^n}=4\)

\(\Rightarrow\dfrac{\left(-2\right)^5}{\left(-2\right)^n}=\left(-2\right)^2\)

\(\Rightarrow\left(-2\right)^n.\left(-2\right)^2=\left(-2\right)^5\)

(-2)n + 2 = (-2)5

n + 2 = 5

n = 5 - 2

n = 3.

b) \(\dfrac{8}{2^n}=2\)

\(\Rightarrow\dfrac{2^3}{2^n}=2\)

\(\Rightarrow\) 2n . 2 = 23

n + 1 = 3

n = 3 - 1

n = 2.

c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)

2n - 1 = 3

2n = 3 + 1

2n = 4

n = 4 : 2

n = 2.

2. Tính:

a) \(\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{4}\right)^2\)

\(=\left(\dfrac{1}{2}\right)^3.\left[\left(\dfrac{1}{2}\right)^2\right]^2\)

\(=\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{2}\right)^4\)

\(=\left(\dfrac{1}{2}\right)^7\)

\(=\dfrac{1}{128}\)

b) 273 : 93

= (33)3 : (32)3

= 39 : 36

= 33

= 27

c) 1252 : 253

= (53)2 : (52)3

= 56 : 56

= 1

d) \(\dfrac{27^2.8^5}{6^6.32^3}\)

\(=\dfrac{\left(3^3\right)^2.\left(2^3\right)^5}{6^6.\left(2^5\right)^3}\)

\(=\dfrac{3^6.2^{15}}{6^6.2^{15}}\)

\(=\dfrac{3^6}{6^6}\)

\(=\dfrac{1}{64}.\)

10 tháng 7 2017

B2 :

b) 27\(^3\): 9\(^3\)= (27:9)\(^3\)= 3\(^3\)

c) 125\(^2\): 25\(^3\)= 15625 : 15625 = 1