(1/2-1)x(1/3-1)x(1/4-1)x...x(1/200-1)
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Đổi 4,2h = 4h 12' 3,25h = 3h 15'
= ( 3h x 7 + 4h + 3h x 3 - 2h ) + ( 15' x 7 + 12' + 15' x 3 - 12' )
= ( 3h x ( 7 + 3 ) + 4h - 2h ) + ( 15' x ( 7 + 3 ) + 12' - 12' )
= 32h + 150'
= 32h + 2h + 30'
= 34h 30'
HT
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\(\left(-\dfrac{1}{4}+\dfrac{7}{33}-\dfrac{5}{3}\right)-\left(-\dfrac{15}{12}+\dfrac{6}{11}-\dfrac{48}{49}\right)\)
=\(\dfrac{1}{4}+\dfrac{7}{33}-\dfrac{5}{3}+\dfrac{15}{12}-\dfrac{6}{11}+\dfrac{48}{49}\)
=\(\left(-\dfrac{1}{4}-\dfrac{5}{3}+\dfrac{5}{12}\right)+\left(\dfrac{7}{33}-\dfrac{6}{11}\right)+\dfrac{48}{49}\)
\(=\left(-\dfrac{23}{12}+\dfrac{15}{12}\right)+\left(\dfrac{7}{33}-\dfrac{18}{33}\right)+\dfrac{48}{49}\)
=\(-\dfrac{2}{3}+\dfrac{-1}{3}+\dfrac{48}{49}\)
=\(-1+\dfrac{48}{49}=-\dfrac{49}{49}+\dfrac{48}{49}=-\dfrac{1}{49}\)
\(\left(\frac{-1}{4}+\frac{7}{33}-\frac{5}{3}\right)-\left(-\frac{15}{12}+\frac{6}{11}-\frac{48}{49}\right)\)
\(=\frac{-1}{4}+\frac{7}{33}-\frac{5}{3}+\frac{15}{12}-\frac{6}{11}+\frac{48}{49}\)
\(=\left(-\frac{1}{4}-\frac{5}{3}+\frac{15}{12}\right)+\left(\frac{7}{33}-\frac{6}{11}\right)+\frac{48}{49}\)
\(=\left(-\frac{23}{12}+\frac{15}{12}\right)+\left(\frac{7}{33}-\frac{18}{33}\right)+\frac{48}{49}\)
\(=-\frac{2}{3}+\frac{-1}{3}+\frac{48}{49}\)
\(=-1+\frac{48}{49}\)
\(=-\frac{49}{49}+\frac{48}{49}\)
\(=-\frac{1}{49}\)
\(\left(\frac{1}{2}-1\right)\times\left(\frac{1}{3}-1\right)\times\left(\frac{1}{4}-1\right)\times...\times\left(\frac{1}{200}-1\right)\)
\(=-\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{200}\right)\)
\(=-\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{199}{200}\)
\(=-\frac{1}{200}\)
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