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AH
Akai Haruma
Giáo viên
15 tháng 7 2023

Lời giải:

$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{x\times (x+1)}=\frac{1}{2}$

$\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{1}{x\times (x+1)}=\frac{1}{2}$

$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{x\times (x+1)}=\frac{1}{2}$
$1-\frac{1}{4}+\frac{1}{x\times (x+1)}=\frac{1}{2}$

$\frac{1}{x\times (x+1)}=\frac{-1}{4}$ (đây là số âm lớp 4 chưa học). Bạn xem lại đề.

25 tháng 2 2020

1/2+4/3*1/6

=1/2+4/18

=13/18

25 tháng 2 2020

1/2 + 4/3 = 3/6 + 8/6 = 11/6

4/5 + 3/4 : 2/3 = 4/5 + 3/4 * 3/2 = 4/5 + 9/8 = 32/40 + 45/40 = 77/40

7/2 - 4/3 * 1/6 = 7/2 - 2/9 = 63/18 - 4/18 = 59/18

4/5 * 4/7 : 2/3 = 16/35 : 2/3 = 16/35 * 3/2 = 24/35

1/4 : 5/3 + 1/6 = 1/4 * 3/5 + 1/6 = 3/20 + 1/6 = 9/60 + 10/60 = 19/60

3 - 4/5 : 1/3 = 3 - 4/5 * 3/1 = 3 - 12/5 = 15/5 - 12/5 = 3/5

5/9 * 2/7 - 3/7 = 10/63 - 3/7 = 10/63 - 27/63 = -17/63  

30 tháng 3 2022

tham khảo:

30 tháng 3 2022

99/100

7 tháng 6 2016

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\)\(\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}\)\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}\)\(\frac{1.2.3}{2.3.4}=\frac{1}{4}\)

\(\left(1+\frac{1}{2}\right):\left(1+\frac{1}{3}\right):\left(1+\frac{1}{4}\right)\)\(\frac{2+1}{2}:\frac{3+1}{3}:\frac{4+1}{4}\)\(\frac{3}{2}:\frac{4}{3}:\frac{5}{4}=\frac{3}{2}.\frac{3}{4}.\frac{4}{5}=\frac{3.3.4}{2.4.5}=\frac{3.3}{2.5}=\frac{9}{10}\)

\(\frac{6}{5}-\frac{4}{5}.\frac{4}{8}+1=\frac{6}{5}+1-\frac{4.4}{5.8}=\frac{6+5}{5}-\frac{4}{5.2}=\frac{11}{5}-\frac{2}{5}=\frac{9}{5}\)
x < \(\frac{3}{4}+\frac{4}{5}=\frac{15}{20}+\frac{16}{20}=\frac{31}{20}=\frac{20}{20}+\frac{11}{20}=1\frac{11}{20}\)=> x = 0 ; 1

\(\frac{1}{2}+\frac{2}{3}< x< 4-\frac{5}{4}\)<=> \(\frac{3}{6}+\frac{4}{6}< x< \frac{16}{4}-\frac{5}{4}\)<=> \(\frac{7}{6}< x< \frac{11}{4}\)=> \(\frac{14}{12}< \frac{12x}{12}< \frac{33}{12}\)

=> 14 < 12x < 33 => 12x = 24 => x = 24 : 12 = 2

23 tháng 8 2019

tra loi nhanh ho mk voi

23 tháng 8 2019

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

    = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

      = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

      = \(1-\frac{1}{7}\)

      =   \(\frac{7}{7}-\frac{1}{7}\)

        = \(\frac{6}{7}\)

2) \(\frac{7}{4}-x.\frac{4}{3}=\frac{5}{19}\)

              \(x.\frac{4}{3}=\frac{7}{4}-\frac{5}{19}\)

         \(x.\frac{4}{3}=\frac{133}{76}-\frac{20}{76}\)

\(x.\frac{4}{3}=\frac{113}{76}\)

      \(x=\frac{113}{76}:\frac{4}{3}\)

      \(x=\frac{399}{304}\)

VẬY \(x=\frac{399}{304}\)

b) \(\left(x+\frac{3}{4}\right).\frac{5}{7}=\frac{10}{9}\)

      \(\left(x+\frac{3}{4}\right)=\frac{10}{9}:\frac{5}{7}\)

     \(x+\frac{3}{4}=\frac{14}{9}\)

              \(x=\frac{14}{9}-\frac{3}{4}\)

               \(x=\frac{29}{36}\)

Vậy \(x=\frac{29}{36}\)

c) \(x.\frac{1}{2}+\frac{3}{2}.x=\frac{4}{5}\)

\(x.\left(\frac{1}{2}+\frac{3}{2}\right)=\frac{4}{5}\)

\(x.2=\frac{4}{5}\)

     \(x=\frac{4}{5}:2\)

      \(x=\frac{2}{5}\)

Vậy \(x=\frac{2}{5}\)

Chúc bạn học tốt !!!

23 tháng 1 2020

                                                                Bài giải

a, \(\frac{4}{5}-\frac{2}{3}+\frac{1}{5}-\frac{1}{3}\)

\(=\left(\frac{4}{5}+\frac{1}{5}\right)-\left(\frac{2}{3}+\frac{1}{3}\right)=1-1=0\)

b, \(\frac{2}{5}\text{ x }\frac{7}{4}-\frac{2}{5}\text{ x }\frac{3}{7}\)

\(=\frac{2}{5}\text{ x }\left(\frac{7}{4}-\frac{3}{7}\right)=\frac{2}{5}\text{ x }\frac{37}{28}=\frac{37}{70}\)

c, \(\frac{13}{4}\text{ x }\frac{2}{3}\text{ x }\frac{4}{13}\text{ x }\frac{3}{12}=\frac{13\text{ x }2\text{ x }4\text{ x }3}{4\text{ x }3\text{ x }13\text{ x }12}=\frac{1}{6}\)

d,  \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)

\(=\frac{3}{4}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{13}{32}\right)\)

\(=1+1+1\)

\(=3\)

e, \(\frac{2}{5}+\frac{6}{9}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\frac{2}{5}+\frac{2}{3}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\frac{1}{5}\left(2+3\right)+\frac{1}{3}\left(2+1\right)+\frac{1}{4}\left(3+1\right)\)

\(=\frac{1}{5}\cdot5+\frac{1}{3}\cdot3+\frac{1}{4}\cdot4\)

\(=1+1+1\)

\(=3\)

23 tháng 1 2020

a, \(\frac{4}{5}-\frac{2}{3}+\frac{1}{5}-\frac{1}{3}\)

\(=\left(\frac{4}{5}+\frac{1}{5}\right)-\left(\frac{2}{3}+\frac{1}{3}\right)=1-1=0\)

b, \(\frac{2}{5}\text{ x }\frac{7}{4}-\frac{2}{5}\text{ x }\frac{3}{7}\)

\(=\frac{2}{5}\text{ x }\left(\frac{7}{4}-\frac{3}{7}\right)=\frac{2}{5}\text{ x }\frac{37}{28}=\frac{37}{70}\)

c, \(\frac{13}{4}\text{ x }\frac{2}{3}\text{ x }\frac{4}{13}\text{ x }\frac{3}{12}=\frac{13\text{ x }2\text{ x }4\text{ x }3}{4\text{ x }3\text{ x }13\text{ x }12}=\frac{1}{6}\)

d,  \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)

\(=\frac{3}{4}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{13}{32}\right)\)

\(=1+1+1\)

\(=3\)

e, \(\frac{2}{5}+\frac{6}{9}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\frac{2}{5}+\frac{2}{3}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\frac{1}{5}\left(2+3\right)+\frac{1}{3}\left(2+1\right)+\frac{1}{4}\left(3+1\right)\)

\(=\frac{1}{5}\cdot5+\frac{1}{3}\cdot3+\frac{1}{4}\cdot4\)

\(=1+1+1\)

\(=3\)

17 tháng 5 2021

Ta có :

(1-1/2).(1-2/3).(1-3/4).(1-4/5)

=1/2.1/3.1/4.1/5

=1/2.3.4.5

=1/120

Lưu ý dấu . là dấu nhân nha 

đó là kiến thức cấp 2 do ko có dấu nhân nên mình dùng tạm 

Đây là câu trả lời nha

17 tháng 5 2021

thui chết kiến thức cấp 2 mà sao lớp 4 đã có đc

4 tháng 3 2019

=3-2/2*3+4-3/3*4+5-4/4*5+6-5/5*6    =3/2*3-2/2*3+4/3*4-3/3*4+5/4*5-4/4*5+6/5*6-5/5*6       =1/2-1/6   =4/12=1/3

18 tháng 4 2022

Mình không hiểu 

 

27 tháng 1 2017

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)

\(=\frac{2}{6}\times\frac{3}{4}\times\frac{4}{5}\)

\(=\frac{1}{4}\times\frac{4}{5}\)

\(=\frac{1}{5}\)

happy new year

27 tháng 1 2017

(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)

=(1/2 x 2/3) x (3/4x4/5).

=1/3x3/5

=1/5