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23 tháng 6

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23 tháng 6

HT.Phong =) thế này đúng nghĩa thầy cô dịch chữ hs

3 tháng 5 2022

a) \(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{2}{5}\right)\times\left(1-\dfrac{2}{7}\right)\times\left(1-\dfrac{2}{9}\right)\)

\(=\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\times\left(\dfrac{5}{5}-\dfrac{2}{5}\right)\times\left(\dfrac{7}{7}-\dfrac{2}{7}\right)\times\left(\dfrac{9}{9}-\dfrac{2}{9}\right)\)

\(=\dfrac{2}{3}\times\dfrac{3}{5}\times\dfrac{5}{7}\times\dfrac{7}{9}\)

\(=\dfrac{2\times3\times5\times7}{3\times5\times7\times9}\)

\(=\dfrac{2}{9}\)

b) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\)

\(=1-\dfrac{1}{9}\)

\(=\dfrac{9}{9}-\dfrac{1}{9}\)

\(=\dfrac{8}{9}\)

3 tháng 5 2022

Sửa câu b)

b) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)

 

Đặt \(A=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)

\(2A=\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}\)

\(2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\)

\(2A=1-\dfrac{1}{9}\)

\(2A=\dfrac{9}{9}-\dfrac{1}{9}\)

\(2A=\dfrac{8}{9}\)

\(A=\dfrac{8}{9}:2\)

\(A=\dfrac{8}{18}\)

\(A=\dfrac{4}{9}\)

Vậy : \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}=\dfrac{4}{9}\)

18 tháng 2 2022

-6/8=-3/2

2/7

Quy đồng được 12/20+-35/20=-23/20

Quy đồng được -10/15+3/15=-7/15

Quy đồng lên được -4/26+-5/26=-9/26

Quy đồng lên được: -12/21+7/21=-5/21 nhé

18 tháng 2 2022

\(\dfrac{-1}{8}+\dfrac{-5}{8}=\dfrac{-6}{8}=\dfrac{-3}{4}\)

\(\dfrac{-3}{7}+\dfrac{5}{7}=\dfrac{2}{7}\)

\(\dfrac{3}{5}+\dfrac{-7}{4}=\dfrac{12}{20}+\dfrac{-35}{20}=\dfrac{-23}{20}\)

\(\dfrac{-2}{3}+\dfrac{1}{5}=\dfrac{-10}{15}+\dfrac{3}{15}=\dfrac{-13}{15}\)

\(\dfrac{2}{13}+\dfrac{-5}{26}=\dfrac{-4}{26}+\dfrac{-5}{26}=\dfrac{-9}{26}\)

\(\dfrac{-4}{7}+\dfrac{1}{3}=\dfrac{-12}{21}+\dfrac{7}{21}=\dfrac{-5}{21}\)

a: \(=\dfrac{-7}{8}\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+3+\dfrac{7}{8}=\dfrac{-7}{8}+\dfrac{7}{8}+3=3\)

b: \(=-\dfrac{8}{5}:\dfrac{5}{3}=-\dfrac{24}{25}\)

c: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{6}{8}=\dfrac{6}{7}-\dfrac{5}{8}=\dfrac{48}{56}-\dfrac{35}{56}=\dfrac{13}{56}\)

 

g: \(=\dfrac{-3}{4}-\dfrac{1}{4}+\dfrac{5}{7}+\dfrac{2}{7}+\dfrac{3}{5}=\dfrac{3}{5}\)

h: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{7}{19}-\dfrac{12}{19}=-\dfrac{5}{19}\)

i: \(=\dfrac{2013}{7}\left(19+\dfrac{5}{8}-26-\dfrac{5}{8}\right)=\dfrac{2013}{7}\cdot\left(-7\right)=-2013\)

a: =-5/7(2/11+9/11)+12/7

=12/7-5/7

=7/7=1

b: \(=\dfrac{-12}{56}+\dfrac{35}{56}-\dfrac{28}{56}=\dfrac{-5}{56}\)

c: \(=\dfrac{1}{4}-\dfrac{5}{13}+\dfrac{2}{11}-\dfrac{8}{13}+\dfrac{3}{4}\)

=1-1+2/11

=2/11

d: \(=\dfrac{21}{31}+\dfrac{-16}{7}+\dfrac{44}{53}+\dfrac{10}{31}+\dfrac{9}{53}\)

=1+1-16/7

=-2/7

e: \(=\dfrac{\dfrac{4}{36}-\dfrac{30}{36}-\dfrac{144}{36}}{\dfrac{21}{36}-\dfrac{1}{36}-\dfrac{360}{36}}=\dfrac{-160}{-340}=\dfrac{8}{17}\)

15 tháng 5 2022

8/9 x 5/4 + 3/5 = 10/9 + 3/5 = 77/45

5/8 + 1/4 = 5/9 + 2/8 = 7/8

1/2 + 5/9 = 9/18 + 5/9 = 14/9

9/8 x 3/4  - 4/7 = 27/32 - 4/7 = 61/224

15 tháng 5 2022

a) \(\dfrac{8}{9}:\dfrac{4}{5}+\dfrac{3}{5}=\dfrac{8}{9}\times\dfrac{5}{4}+\dfrac{2}{5}=\dfrac{10}{9}+\dfrac{2}{5}=\dfrac{50}{45}+\dfrac{18}{45}=\dfrac{68}{45}\)

b) \(\dfrac{5}{8}+\dfrac{1}{4}=\dfrac{5}{8}+\dfrac{2}{8}=\dfrac{6}{8}=\dfrac{3}{4}\)

c) \(\dfrac{7}{8}\times\dfrac{4}{7}+\dfrac{5}{9}=\dfrac{1}{2}+\dfrac{5}{9}=\dfrac{9}{18}+\dfrac{10}{18}=\dfrac{19}{18}\)

d) \(\dfrac{9}{8}:\dfrac{4}{3}-\dfrac{4}{7}=\dfrac{9}{8}\times\dfrac{3}{4}-\dfrac{4}{7}=\dfrac{27}{32}-\dfrac{4}{7}=\dfrac{61}{244}\)

\(I=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{199\cdot201}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{199\cdot201}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{199}-\dfrac{1}{201}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{200}{201}=\dfrac{100}{201}\)

AH
Akai Haruma
Giáo viên
6 tháng 10 2021

Lời giải:

\(2\times I=\frac{2}{1\times 3}+\frac{2}{3\times 5}+\frac{2}{5\times 7}+...+\frac{2}{199\times 201}\)

\(=\frac{3-1}{1\times 3}+\frac{5-3}{3\times 5}+\frac{7-5}{5\times 7}+....+\frac{201-199}{199\times 201}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\)

\(=1-\frac{1}{201}=\frac{200}{201}\)

\(I=\frac{200}{201}:2=\frac{100}{201}\)

23 tháng 8 2023

a) \(\dfrac{12}{15}< 1\)

b) \(\dfrac{9}{7}>1\)

c) \(\dfrac{3}{3}=1\)

d) \(\dfrac{99}{100}>1\)

23 tháng 8 2023

a) \(\dfrac{12}{15}\) < 1

b) \(\dfrac{9}{7}\) > 1

c)  \(\dfrac{3}{3}\) = 1

d) \(\dfrac{99}{100}\)  < 1

8 tháng 4 2023

\(\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}}{1\dfrac{1}{6}-\dfrac{7}{8}+0,7}\\ =\dfrac{2\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{11}\right)}{7\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{11}\right)}-\dfrac{\dfrac{2}{6}-\dfrac{2}{8}+\dfrac{2}{10}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}\\ =\dfrac{2}{7}-\dfrac{2\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{10}\right)}{7\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}\\ =\dfrac{2}{7}-\dfrac{2}{7}=0\)

8 tháng 4 2023

phân số cuối là \(\dfrac{2}{7}-\dfrac{2\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{10}\right)}{7\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{10}\right)}\) nha :vv