Tính:
1. A = 2/3 + 5/6 : 5 - 1/18 . (-3)
2. B = 3 { 5 [ (52 + 23) : 11 ] - 16 } + 2015
3. C = ( 1 + 1/1.3 ).( + 1/2.4 ).( 1+ 1/3.5 )...( 1 + 1/2014.2016 )
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A = 13/21.2/11 + 13/21.9/11 + 8/21
= (13/21) + (13/21) + (8/21)
= (13 + 13 + 8)/21
= 34/21
B = (1 - 1/5)(1 - 2/5)(1 - 3/5)...(1 - 9/5)
= (4/5)(3/5)(2/5)(1/5)(0/5)(-1/5)(-2/5)(-3/5)(-4/5)
= 0
C = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/50)
= (1/2)(2/3)(3/4)(4/5)...(49/50)
= 1/50
D = (2^2/1.3) * (3^2/2.4) * (4^2/3.5) * (5^2/4.6) * (6^2/5.7)
= (4/3) * (9/8) * (16/15) * (25/23) * (36/35)
= 0.979
\(5^x=125\)
\(5^x=5^3\)
=> x=3 ( vì cơ số 5>1)
\(3^2.x=81\)
\(9x=81\)
\(x=81:9\)
\(x=9\)
a.
\(\frac{6}{7}+\frac{5}{8}\div5-\frac{3}{16}\times\left(-2\right)^2=\frac{6}{7}+\frac{5}{8}\times\frac{1}{5}-\frac{3}{16}\times4=\frac{6}{7}+\frac{1}{8}-\frac{3}{4}=\frac{48}{56}+\frac{7}{56}-\frac{42}{56}=\frac{13}{56}\)
b.
\(\frac{2}{3}+\frac{1}{3}\times\left(-\frac{4}{9}+\frac{5}{6}\right)\div\frac{7}{12}=\frac{2}{3}+\frac{1}{3}\times\left(-\frac{8}{18}+\frac{15}{18}\right)\times\frac{12}{7}=\frac{2}{3}+\frac{7}{18}\times\frac{4}{7}=\frac{2}{3}+\frac{2}{9}=\frac{6}{9}+\frac{2}{9}=\frac{8}{9}\)
c.
\(\left[6+\left(\frac{1}{3}\right)^3-\left|-2\right|\right]\div\frac{3}{2}=\left(6+\frac{1^3}{3^3}-2\right)\times\frac{2}{3}=\left(4+\frac{1}{27}\right)\times\frac{2}{3}=\left(\frac{108}{27}+\frac{1}{27}\right)\times\frac{2}{3}=\frac{109}{27}\times\frac{2}{3}=\frac{218}{81}\)
d.
\(\left(-2\right)^3\times\left(-\frac{1}{24}\right)+\left(\frac{4}{3}-\frac{11}{6}\right)\div\frac{5}{12}\)\(=\left(-8\right)\times\left(-\frac{1}{24}\right)+\left(\frac{8}{6}-\frac{11}{6}\right)\times\frac{12}{5}=\frac{1}{3}+\left(-\frac{3}{6}\right)\times\frac{12}{5}=\frac{1}{3}-\frac{6}{5}=\frac{5}{15}-\frac{18}{15}\)\(=-\frac{13}{15}\)
Bài 2:
a) \(\frac{2}{3}\) - 4 .(\(\frac{1}{2}\) + \(\frac{3}{4}\)) = \(\frac{2}{3}\) - 4 . \(\frac{5}{4}\)
= \(\frac{2}{3}\) - 5 = \(\frac{-13}{3}\)
b) (\(\frac{-1}{3}\) + \(\frac{5}{6}\)) . 11 - 7 = \(\frac{1}{2}\). 11 - 7
= \(\frac{11}{2}\)- 7 = \(\frac{-3}{2}\)
c) \(\frac{-5}{9}\). \(\frac{3}{11}\)+ (\(\frac{-13}{18}\)) . \(\frac{3}{11}\)= \(\frac{3}{11}\). (\(\frac{-5}{9}\)- \(\frac{13}{18}\))
= \(\frac{3}{11}\). (\(\frac{-23}{18}\))= \(\frac{-23}{66}\)
d) \(\frac{-2}{3}\) . \(\frac{3}{11}\)+ (\(\frac{-16}{9}\)) . \(\frac{3}{11}\)= \(\frac{3}{11}\). (\(\frac{-2}{3}\)- \(\frac{16}{9}\))
= \(\frac{3}{11}\). (\(\frac{-22}{9}\)) = \(\frac{-2}{3}\)
Bài 1:
a) =\(\frac{-1}{2}\)+ \(\frac{3}{5}\)- \(\frac{1}{9}\)+ \(\frac{1}{71}\) + \(\frac{2}{7}\) + \(\frac{4}{35}\)- \(\frac{7}{18}\)
= (\(\frac{-1}{2}\)- \(\frac{1}{9}\)- \(\frac{7}{18}\)) + ( \(\frac{3}{5}\)+ \(\frac{2}{7}\)+ \(\frac{4}{35}\)) + \(\frac{1}{71}\)
= -1 + 1 + \(\frac{1}{71}\)= \(\frac{1}{71}\)
b) = 3 - \(\frac{1}{4}\)+ \(\frac{2}{3}\)- 5 + \(\frac{1}{3}\)+ \(\frac{6}{5}\)- 6 + \(\frac{7}{4}\)- \(\frac{3}{2}\)
= (3 - 5 - 6) + (\(\frac{-1}{4}\)+ \(\frac{7}{4}\)- \(\frac{3}{2}\)) + (\(\frac{2}{3}\)+ \(\frac{1}{3}\)) + \(\frac{6}{5}\)
= -8 + 0 + 1 + \(\frac{6}{5}\)
= \(\frac{-29}{5}\)
a: \(A=\dfrac{2}{3}+\dfrac{5}{6}\cdot\dfrac{1}{5}+\dfrac{1}{18}\cdot3=\dfrac{2}{3}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{2}{3}+\dfrac{2}{6}=\dfrac{4}{6}+\dfrac{2}{6}=1\)
b: \(B=3\cdot\left\{5\cdot\left[33:11\right]-16\right\}+2015\)
\(=3\cdot\left(5\cdot3-16\right)+2015=2015-3=2012\)