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1-2+3-4+5-6+...+2011-2012
=2012-2011+...+6-5+4-3+2-1
=(2012-2001)+...+(6-5)+(4-3)+(2-1)
=1+1+1+...+1+1(có 1006 số 1)
=1x60
=60
= -4/3 - 17/6 . 6/11 + 3 : 1/20
= - 4/3 - 17/11 + 60
= 1885/33
a)
i.Ta có: BCNN(12, 30) = 60
60 : 12 = 5; 60 : 30 = 2. Do đó:
\(\frac{5}{{12}} = \frac{{5.5}}{{12.5}} = \frac{{25}}{{60}}\) và \(\frac{7}{{30}} = \frac{{7.2}}{{30.2}} = \frac{{14}}{{60}}.\)
ii.Ta có: BCNN(2, 5, 8) = 40
40 : 2 = 20; 40 : 5 = 8; 40 : 8 = 5. Do đó:
\(\frac{1}{2} = \frac{{1.20}}{{2.20}} = \frac{{20}}{{40}}\)
\(\frac{3}{5} = \frac{{3.8}}{{5.8}} = \frac{{24}}{{40}}\)
\(\frac{5}{8} = \frac{{5.5}}{{8.5}} = \frac{{25}}{{40}}\).
b)
i.Ta có: BCNN(6, 8) = 24
24 : 6 = 4; 24: 8 = 3. Do đó
\(\begin{array}{l}\frac{1}{6} + \frac{5}{8} = \frac{{1.4}}{{6.4}} + \frac{{5.3}}{{8.3}}\\ = \frac{4}{{24}} + \frac{{15}}{{24}} = \frac{{19}}{{24}}.\end{array}\)
ii. Ta có: BCNN(24, 30) = 120
120: 24 = 5; 120: 30 = 4. Do đó:
\(\begin{array}{l}\frac{{11}}{{24}} - \frac{7}{{30}} = \frac{{11.5}}{{24.5}} - \frac{{7.4}}{{30.4}}\\ = \frac{{55}}{{120}} - \frac{{28}}{{120}} = \frac{{27}}{{120}} = \frac{9}{{40}}\end{array}\)
\(6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(=\frac{77}{12}:\frac{11}{4}+\frac{45}{4}.\left(\frac{5}{15}-\frac{3}{15}\right)\)
\(=\frac{77}{12}.\frac{4}{11}+\frac{45}{4}.\frac{2}{15}\)
\(=\frac{7}{3}+\frac{3}{2}\)
\(=\frac{14}{6}+\frac{9}{6}\)
\(=\frac{23}{6}=3\frac{5}{6}\)
a, \(\dfrac{3}{5}\). (\(-\dfrac{9}{11}\)) + \(\dfrac{-3}{5}\).\(\dfrac{2}{11}\) + \(\dfrac{3}{5}\)
= \(\dfrac{3}{5}\).( - \(\dfrac{9}{11}\) - \(\dfrac{2}{11}\) + 1)
= \(\dfrac{3}{5}\).(- \(\dfrac{11}{11}\) + 1)
= \(\dfrac{3}{5}\).(1-1)
= \(\dfrac{3}{5}\).0
= 0
a. \(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
\(=1.\frac{7}{12}:\frac{7}{12}\)
\(=1\)
b.
\(\frac{5}{9}.\frac{8}{11}+\frac{5}{9}.\frac{9}{11}-\frac{5}{9}.\frac{6}{11}\)
\(=\frac{5}{9}.\left(\frac{8}{11}+\frac{9}{11}-\frac{6}{11}\right)\)
\(=\frac{5}{9}.1\)
\(=\frac{5}{9}\)
Tk mk nha!
b) \(=\frac{5}{9}.\left(\frac{8}{11}+\frac{9}{11}-\frac{6}{11}\right)\)
\(=\frac{5}{9}.1\)
\(=\frac{5}{9}\)
A=33. \(\left(1-\frac{2}{3}\right)\left(1-\frac{2}{5}\right)...\left(1-\frac{2}{99}\right)\)
A=33.\(\frac{1}{3}.\frac{3}{5}....\frac{97}{99}\)
A=33.\(\frac{1}{99}\)
A=\(\frac{33}{99}=\frac{1}{3}\)
Ta có: \(2\frac{1}{3}+\frac{11}{5}:33-\frac{1}{50}.\left(-5\right)^2\)
\(=\frac{7}{3}+\frac{11}{5}.\frac{1}{33}-\frac{1}{50}.25\)
\(=\frac{7}{3}+\frac{11}{165}-\frac{25}{50}\)
\(=\frac{7}{3}+\frac{1}{15}-\frac{1}{2}\)
\(=\frac{70}{30}+\frac{2}{30}-\frac{15}{30}\)
\(=\frac{56}{30}=\frac{28}{15}\)