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25 tháng 6 2018
a) \(\frac{18}{45}-\frac{4}{12}-\frac{6}{9}-\frac{21}{35}=\frac{2}{5}-\frac{1}{3}-\frac{2}{3}-\frac{3}{5}\)
\(=\left(\frac{2}{5}-\frac{3}{5}\right)-\left(\frac{1}{3}+\frac{2}{3}\right)\)
\(=\frac{-1}{3}-1\)
\(=\frac{-4}{3}\)
b) \(\frac{4}{3}+\frac{3}{5}+\frac{7}{3}+\frac{2}{5}+\frac{1}{3}=\left(\frac{4}{3}+\frac{7}{3}+\frac{1}{3}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\)
\(=4+1=5\)
c) \(\frac{1}{3}.\frac{4}{5}.\frac{1}{3}.\frac{6}{5}=\frac{8}{75}\)
d) \(\frac{6}{7}.\frac{8}{13}+\frac{6}{7}.\frac{9}{13}-\frac{3}{13}.\frac{6}{7}\)
\(=\frac{6}{7}.\left(\frac{8}{13}+\frac{9}{13}-\frac{3}{13}\right)\)
\(=\frac{6}{7}.\frac{14}{13}\)
\(=\frac{12}{13}\)
18 tháng 4 2023
\(1,-\dfrac{4}{7}+\dfrac{2}{3}\times\dfrac{-9}{14}\)
\(=\dfrac{-4}{7}+\dfrac{-18}{42}\)
\(=\dfrac{-4\times6}{7\times6}+\dfrac{-18}{42}\)
\(=\dfrac{-20}{42}+\dfrac{-18}{42}\)
\(=-\dfrac{38}{42}\)
\(=-\dfrac{19}{21}\)
\(2,\dfrac{17}{13}-\left(\dfrac{4}{13}-11\right)\)
\(=\dfrac{17}{13}-\dfrac{4}{13}+11\)
\(=\dfrac{13}{13}+11\)
\(=1+11\)
\(=12\)
\(3,8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\)
\(=\dfrac{58}{7}-\left(\dfrac{31}{9}+\dfrac{30}{7}\right)\)
\(=\dfrac{58}{7}-\dfrac{31}{9}-\dfrac{30}{7}\)
\(=\dfrac{58}{7}-\dfrac{30}{7}-\dfrac{31}{9}\)
\(=\dfrac{28}{7}-\dfrac{31}{9}\)
\(=\dfrac{28\times9}{7\times9}-\dfrac{31\times7}{9\times7}\)
\(=\dfrac{252}{63}-\dfrac{217}{63}\)
\(=\dfrac{35}{63}\)
\(=\dfrac{5}{9}\)
\(5,\left(\dfrac{2}{3}-1\dfrac{1}{2}\right):\dfrac{4}{3}+\dfrac{1}{2}\)
\(=\left(\dfrac{2}{3}-\dfrac{3}{2}\right):\dfrac{4}{3}+\dfrac{1}{2}\)
\(=\left(\dfrac{2\times2}{3\times2}-\dfrac{3\times3}{2\times3}\right):\dfrac{4}{3}+\dfrac{1}{2}\)
\(=\left(\dfrac{4}{6}-\dfrac{9}{6}\right):\dfrac{4}{3}+\dfrac{1}{2}\)
\(=\dfrac{-5}{6}:\dfrac{4}{3}+\dfrac{1}{2}\)
\(=\dfrac{-5}{6}\times\dfrac{3}{4}+\dfrac{1}{2}\)
\(=\dfrac{-15}{24}+\dfrac{1}{2}\)
\(=\dfrac{-15}{24}+\dfrac{1\times12}{2\times12}\)
\(=\dfrac{-15}{24}+\dfrac{12}{24}\)
\(=\dfrac{-3}{24}\)
\(=-\dfrac{1}{8}\)
\(6,\dfrac{-5}{13}+\dfrac{2}{5}+\dfrac{-8}{13}+\dfrac{3}{5}-\dfrac{3}{7}\)
\(=\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{3}{7}\)
\(=\dfrac{-13}{13}+\dfrac{5}{5}-\dfrac{3}{7}\)
\(=-1+1-\dfrac{3}{7}\)
\(=-\dfrac{3}{7}\)
\(7,\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}:\dfrac{7}{10}+\dfrac{6}{5}\)
\(=\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}\times\dfrac{10}{7}+\dfrac{6}{5}\)
\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+1\right)\)
\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{1\times7}{1\times7}\right)\)
\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{7}{7}\right)\)
\(=\dfrac{6}{5}\times\dfrac{20}{7}\)
\(=\dfrac{120}{35}\)
\(=\dfrac{24}{7}\)
13 tháng 1 2018
Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha
1, 7A = 7+7^2+7^3+....+7^2008
6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1
=> A = (7^2008-1)/6
Tk mk nha
13 tháng 1 2018
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)
\(\Rightarrow6A=7^{2008}-1\)
\(\Rightarrow A=\frac{7^{2008}-1}{6}\)
YN
3
S
16 tháng 4 2023
a/\(\dfrac{26}{15}+-\dfrac{7}{13}+-\dfrac{6}{13}-\dfrac{11}{15}\)
\(=\left(\dfrac{26}{15}-\dfrac{11}{15}\right)-\left(\dfrac{7}{13}+\dfrac{6}{13}\right)\)
\(=1-1\)
\(=0\)
b/Sửa đề:
\(-\dfrac{3}{4}\cdot\dfrac{4}{13}+-\dfrac{3}{4}\cdot\dfrac{9}{13}+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}\cdot\left(\dfrac{4}{13}+\dfrac{9}{13}\right)+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}\cdot1+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}+\dfrac{3}{4}\)
\(=0\)
15 tháng 4 2019
\(\left(19\frac{5}{8}:\frac{7}{12}-13\frac{1}{4}:\frac{7}{12}\right).\frac{4}{5}\)
\(=\left(\frac{157}{8}:\frac{7}{12}-\frac{53}{4}:\frac{7}{12}\right).\frac{4}{5}\)
\(=\left[\left(\frac{157}{8}-\frac{53}{4}\right):\frac{7}{12}\right].\frac{4}{5}\)
\(=\left[\frac{51}{8}:\frac{7}{12}\right].\frac{4}{5}\)
\(=\frac{153}{14}.\frac{4}{5}\)
\(=\frac{306}{35}\)
15 tháng 4 2019
\(\left(\frac{-2}{5}+\frac{3}{7}\right)-\left(\frac{4}{9}+\frac{12}{20}-\frac{13}{35}\right)+\frac{7}{35}\)
\(=\frac{1}{35}-\frac{212}{315}+\frac{7}{35}\)
\(=\frac{1}{35}+\frac{-212}{315}+\frac{7}{35}\)
\(=\frac{9}{315}+\frac{-212}{315}+\frac{63}{315}\)
\(=\frac{-140}{315}=\frac{-4}{9}\)
3 tháng 7 2022
a: \(=\left(\dfrac{5}{6}+\dfrac{3}{4}-\dfrac{9}{10}\right):\left(\dfrac{5}{6}-\dfrac{3}{4}+\dfrac{9}{10}\right)\)
\(=\dfrac{50+45-54}{60}:\dfrac{50-45+54}{60}\)
\(=\dfrac{41}{59}\)
b: \(=13+\dfrac{7}{12}+4+\dfrac{3}{10}-8-\dfrac{7}{10}=\dfrac{3}{10}+1=\dfrac{13}{10}\)
c: \(=31+\dfrac{4}{17}-8-\dfrac{5}{13}-11-\dfrac{8}{13}\)
\(=11+\dfrac{4}{17}=\dfrac{191}{17}\)
1 tháng 5 2021
-3/11.(-22)/66.121/15
=(-3).(-22).121
11.66.15
=11
15
3/7.2/5.7/3.20.19/72
=3.2.7.20.19
7.5.3.72
=76
16
6/7.8/13+6/13.9/7-3/13.6/7
=6/7.8/13+6/7.9/13-3/13.6/7
=6/7.(8/13+9/13-3/13)
=6/7.14/13
=12/13
-1/4.152/11+68/4.(-1)/11
=152/4.(-1)/11+68/4.(-1)/11
=(-1)/11.(152/4+68/4)
=(-1)/11.220/4
=-110/22
-5/7.2/11+(-5)/7.9/11+12/7
=-5/7.2/11+-5/7.9/11+12/7
=-5/7.(2/11+9/11)+12/7
=-5/7.1+12/7
=(-5)/7+12/7
=7/7
=1
146/13-(18/7+68/13)
=146/13-18/7-68/13
=(146/13-68/13)-18/7
=78/13-18/7
=6-18/7
=42/7-18/7
=24/7
3/4x7/13+3/4x6/13
=3/4x(7/13+6/13)
=3/4x13/13
=3/4x1
=3/4