Tính S = 1 / 5 x 9 + 1 / 9 x 13 + 1 / 13 x 17 + ....... + 1 / 41 x 45
Giải thích giúp tôi nếu trong phép tính có 1 / 4
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Tính S = 1/5 x 9 + 1/9 x 13 + 1/13 x 17+ ........+ 1/41 x 45
\(4.S=\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\)
\(4S=\frac{1}{5}-\frac{1}{6}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\)
\(4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\)
\(S=\frac{8}{45}:4=\frac{2}{45}\)
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\(S=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{41.45}\)
\(\Rightarrow4S=\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\)
\(\Rightarrow4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\)
\(\Rightarrow4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\Rightarrow S=\frac{8}{45}:4=\frac{2}{45}\)
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Thực hiện phép tính (Tính hợp lý nếu có thể)
a) -10/13 + 5/17 – 3/13 + 12/17 – 11/20
b) 3/4 + -5/6 – 11/-12
c) [13. 4/9 + 2. 1/9] – 3. 4/9
d) 1,25 : 15/20 + [25% – 5/6] : 4. 2/3
Tìm x, biết
a)x – 1/3 = 5/14 . -7/6
b) 3/4 + 1/4 x = 0,2
c) 1/12 .x2 = 1. 1/3
a; - \(\dfrac{10}{13}\) + \(\dfrac{5}{17}\) - \(\dfrac{3}{13}\) + \(\dfrac{12}{17}\) - \(\dfrac{11}{20}\)
= - (\(\dfrac{10}{13}\) + \(\dfrac{3}{13}\)) + (\(\dfrac{5}{17}\) + \(\dfrac{12}{17}\)) - \(\dfrac{11}{20}\)
= - 1 + 1 - \(\dfrac{11}{20}\)
= 0 - \(\dfrac{11}{20}\)
= - \(\dfrac{11}{20}\)
b; \(\dfrac{3}{4}\) + \(\dfrac{-5}{6}\) - \(\dfrac{11}{-12}\)
= \(\dfrac{9}{12}\) - \(\dfrac{10}{12}\) + \(\dfrac{11}{12}\)
= \(\dfrac{10}{12}\)
= \(\dfrac{5}{6}\)
c; [13.\(\dfrac{4}{9}\) + 2.\(\dfrac{1}{9}\)] - 3.\(\dfrac{4}{9}\)
= [\(\dfrac{52}{9}\) + \(\dfrac{2}{9}\)] - \(\dfrac{4}{3}\)
= \(\dfrac{54}{9}\) - \(\dfrac{4}{3}\)
= \(\dfrac{14}{3}\)
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d; 1,25 : \(\dfrac{15}{20}\) + [25% - \(\dfrac{5}{6}\)] : 4.\(\dfrac{2}{3}\)
= 1,25 x \(\dfrac{20}{15}\) + [\(\dfrac{1}{4}\) - \(\dfrac{5}{6}\)] : 4.\(\dfrac{2}{3}\)
= \(\dfrac{5}{3}\) - \(\dfrac{7}{12}\) : 4 x \(\dfrac{2}{3}\)
= \(\dfrac{5}{3}\) - \(\dfrac{7}{48}\).\(\dfrac{2}{3}\)
= \(\dfrac{5}{3}\) - \(\dfrac{7}{72}\)
= \(\dfrac{113}{72}\)
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Xem thêm câu trả lời
1.thực hiện phép tính:
a,5/13 + -5/7 + -20/41 + 8/13 + -21/41
b,-5/7 . 2/11 + -5/7 . 9/11 +1
c, (4/5 + 1/2) . (3/13 - 8/13)
2. a, x + 4/7=7/11
b, -5/6 - x = 7/12 + -1/3
c,x - 1/4 = 5/8 . 2/3
d,x/126 = -5/9 . 4/7
giúp mik vs mn ơi, mik đnag cần rất gấp
Bài 1: Thực hiện các phép tính (Tính nhanh nếu có thể)a) dfrac{-5}{9} - dfrac{-5}{12} b) dfrac{-5}{12} : dfrac{15}{4} c) dfrac{1}{13} x dfrac{8}{13} + dfrac{5}{13} x dfrac{1}{13} - dfrac{14}{13}Bài 2: Tìm x, biết:a) xdfrac{1}{5}+dfrac{-3}{7} b) dfrac{3}{5}-dfrac{4}{7}:xdfrac{-9}{10} c) x-left(dfrac{-3}{4}right)dfrac{-2}{3}-dfrac{1}{2}d) dfrac{-5}{9}-xdfrac{1}{3}+dfrac{7}{18}Bài 3: Cho S dfrac{1}{2^2}+dfrac{1}{3...
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Bài 1: Thực hiện các phép tính (Tính nhanh nếu có thể)
a) \(\dfrac{-5}{9}\) - \(\dfrac{-5}{12}\) b) \(\dfrac{-5}{12}\) : \(\dfrac{15}{4}\) c) \(\dfrac{1}{13}\) x \(\dfrac{8}{13}\) + \(\dfrac{5}{13}\) x \(\dfrac{1}{13}\) - \(\dfrac{14}{13}\)
Bài 2: Tìm \(x\), biết:
a) \(x=\dfrac{1}{5}+\dfrac{-3}{7}\) b) \(\dfrac{3}{5}-\dfrac{4}{7}\)\(:\)\(x=\dfrac{-9}{10}\) c) \(x-\left(\dfrac{-3}{4}\right)=\dfrac{-2}{3}-\dfrac{1}{2}\)
d) \(\dfrac{-5}{9}-x=\dfrac{1}{3}+\dfrac{7}{18}\)
Bài 3: Cho S = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{10^2}\). Chứng minh rằng: \(S>\dfrac{9}{22}\)
Bài 1 : thực hiện các phép tính ( tính hợp lí nếu có thể ):a ,dfrac{7}{2}.dfrac{8}{13}+dfrac{8}{13}.dfrac{-5}{2}+dfrac{8}{13}b , dfrac{-5}{17}.dfrac{-9}{23}+dfrac{9}{23}.dfrac{-22}{17}+11dfrac{9}{23}Bài 2 : tìm x , biết :a , dfrac{7}{8}+xdfrac{3}{5}b , dfrac{1}{3}:left(2x-1right)dfrac{-4}{24}
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Bài 1 : thực hiện các phép tính ( tính hợp lí nếu có thể ):
a ,\(\dfrac{7}{2}.\dfrac{8}{13}+\dfrac{8}{13}.\dfrac{-5}{2}+\dfrac{8}{13}\)
b , \(\dfrac{-5}{17}.\dfrac{-9}{23}+\dfrac{9}{23}.\dfrac{-22}{17}+11\dfrac{9}{23}\)
Bài 2 : tìm x , biết :
a , \(\dfrac{7}{8}+x=\dfrac{3}{5}\)
b , \(\dfrac{1}{3}:\left(2x-1\right)=\dfrac{-4}{24}\)
Bài 2 :
a, \(x=\dfrac{3}{5}-\dfrac{7}{8}=\dfrac{24-30}{40}=-\dfrac{6}{40}=-\dfrac{3}{20}\)
b, \(2x-1=-2\Leftrightarrow x=-\dfrac{1}{2}\)
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tính nhanh 4/1 x 5+ 4/5 x 9 + 4/9 x 13+⋯+4/41 x 45 + 4/45 x 49
tìm x biết
a,x\2008 - 1\10 -1\15 -1\21 - ...-1\120 = 5\8
b,7\x + 4\5*9 + 4\9*13 + 4\ 13*17 +...+4\41*45=29\45
Tính bằng cách thuận tiên nhất:1):(3/4 x 5/97 + 1/9 x 13/47) x (1/5 - 7/25 x 5/7)2): 8/17 x 4/15 + 8/17 x 22/15 - 8/15 x 9/173): 2021/2 x 1/3 + 4042/4 x 1/5 + 6063/3 x 22/154); 4/7 x 2/13 + 8/13 :7/4 + 4/7 : 13/2 + 4/7 x 1/135): 2022 x 2021 - 1/ 2021 + 2022 x 20206): 18 x 123 + 9 x 4567 x 2 + 3 x 5310 x 6 / (2 + 4 + 6 + 8 + ...+20 + 22) + 487): A 2021 x 2021 x 202020 - 2020 x 2020 x 20212021 / 2020 x 201920...
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Tính bằng cách thuận tiên nhất:
1):(3/4 x 5/97 + 1/9 x 13/47) x (1/5 - 7/25 x 5/7)
2): 8/17 x 4/15 + 8/17 x 22/15 - 8/15 x 9/17
3): 2021/2 x 1/3 + 4042/4 x 1/5 + 6063/3 x 22/15
4); 4/7 x 2/13 + 8/13 :7/4 + 4/7 : 13/2 + 4/7 x 1/13
5): 2022 x 2021 - 1/ 2021 + 2022 x 2020
6): 18 x 123 + 9 x 4567 x 2 + 3 x 5310 x 6 / (2 + 4 + 6 + 8 + ...+20 + 22) + 48
7): A= 2021 x 2021 x 202020 - 2020 x 2020 x 20212021 / 2020 x 20192019
1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)
\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)
=0
2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)
\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)
\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)
3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)
\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)
\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)
\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)
\(=\dfrac{52546}{15}\)
4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)
\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)
\(=\dfrac{4}{7}\)
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thực hiện phép tính :
a, -1/2 + 19/23+ -9/2+ 4/23 +3 /-6
b. 5/13+ -5/7 +-20/41 + 8/13 +-21/41
c.-5/7 x 19/41 + 5/7 x -21/41 + 5/7
d. 7/3 +1/2 - -3/70
Đây là phân số
