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\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)
\(\left(1-\frac{2}{5}\right)\times\left(1-\frac{2}{7}\right)\times\left(1-\frac{2}{9}\right)\times\left(1-\frac{2}{11}\right)\times\left(1-\frac{2}{13}\right)\)
\(=\frac{3}{5}\times\frac{5}{7}\times\frac{7}{9}\times\frac{9}{11}\times\frac{11}{13}=\frac{3}{13}\)
a, \(\overline{xx}+x+5=125\)
\(x\times11+x=120\)
\(x\left(1+11\right)=120\)
\(x=120\div12\)
\(x=10\)
Vậy x = 10
\(\overline{xxx}+\overline{xx}+x+x=992\)
\(x\times111+x\times11+x\times2=992\)
\(x\left(111+11+2\right)=992\)
\(x=992\div124\)
\(x=8\)
Vậy x = 8
\(4725+\overline{xxx}+\overline{xx}+x=54909\)
\(x\times111+x\times11+x=50184\)
\(x\left(111+11+1\right)=50184\)
\(x\times123=50184\)
\(x=408\)
Vậy x = 408
b, \(\overline{xxx}-\overline{xx}-x-25=4430\)
\(x\times111-x\times11-x=4455\)
\(x\left(111-11-1\right)=4455\)
\(x=4455\div99\)
\(x=45\)
Vậy x = 45
\(\overline{xxx}+\overline{xx}+x+x+x+1=1001\)
\(x\times111+x\times11+x\times3=1000\)
\(x\left(111+11+3\right)=1000\)
\(x=1000\div125\)
\(x=8\)
Vậy x = 8
\(35655-\overline{xxx}-\overline{xx}-x=5274\)
\(x\times111+x\times11+x=30381\)
\(x\left(111+11+1\right)=30381\)
\(x=30381\div123\)\
\(x=247\)
Vậy \(x=247\)
(1-1/2)×(1-1/3)×(1-1/4 )×...×(1-1/2006)×(1-1/2007)
=(2/2-1/2)×(3/3-1/3)×(4/4-1/4)×..×(2006/2006-1/2006)×(2007/2007-1/2007)
=1/2×2/3×3/4×..×2005/2006×2006/2007
=1/2007
a) \(\frac{3}{5}\times y+\frac{1}{2}:\frac{5}{3}-\frac{5}{4}=\frac{1}{2}\times\frac{1}{3}\)
\(\Rightarrow\frac{3}{5}\times y+\frac{3}{10}-\frac{5}{4}=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y+\left(-\frac{19}{20}\right)=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{67}{60}\)
\(\Rightarrow y=\frac{67}{36}\)
b) \(\frac{4}{5}:y+\frac{1}{4}\times\frac{1}{6}-\frac{1}{2}=\frac{1}{3}\times\frac{5}{2}\)
\(\Rightarrow\frac{4}{5}:y+\frac{1}{24}-\frac{1}{2}=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y+\left(-\frac{11}{24}\right)=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y=\frac{5}{6}+\frac{11}{24}=\frac{31}{24}\)
\(\Rightarrow y=\frac{4}{5}:\frac{31}{24}=\frac{96}{155}\)
c) \(\frac{3}{5}\times y-\frac{4}{5}:3+\frac{1}{12}=\frac{3}{2}+\frac{1}{5}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}+\frac{1}{12}=\frac{17}{10}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}=\frac{97}{60}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{113}{60}\)
\(\Rightarrow y=\frac{113}{36}\)
\(\left(2.8x-32\right):\frac{2}{3}=90\)
\(2.8\cdot x-32=90\cdot\frac{2}{3}\)
\(\frac{14}{5}x-32=60\)
\(\frac{14}{5}x=60+32\)
\(\frac{14}{5}x=92\)
\(x=\frac{230}{7}\)
B , c , d tương tự
Mình làm luôn ko chép lại đề nhé
= ( \(\frac{1}{3}+\frac{3}{3}\)) x ( \(\frac{1}{4}+\frac{4}{4}\)) x ... x ( \(\frac{1}{16}+\frac{16}{16}\))
= \(\frac{4}{3}x\frac{5}{4}x...x\frac{17}{16}\)
= \(\frac{4x5x6x...x17}{3x4x5x...x16}\)
= \(\frac{17}{3}\)
\(\frac{1}{2}\) x 24 + \(\frac{1}{2}\)x 75 + \(\frac{1}{2}\)
= \(\frac{1}{2}\) x 24 + \(\frac{1}{2}\)x 75 + \(\frac{1}{2}\) x 1
= \(\frac{1}{2}\)x ( 24 + 75 + 1 )
= \(\frac{1}{2}\) x 100
= 50
\(\frac{1}{2}\times24+\frac{1}{2}\times75+\frac{1}{2}\)
\(=\frac{1}{2}\times\left(24+75+1\right)\)
\(=\frac{1}{2}\times100\)
\(=50\)
kick mk đi mk kick lại
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right)...\left(1-\frac{1}{2016}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{2015}{2016}\)
\(=\frac{1.2.3.4...2015}{2.3.4.5...2016}\)
\(=\frac{1}{2016}\)
\(=\frac{1}{2}\)