Cho M = 17 5 . − 31 125 . 1 2 . 10 17 . − 1 2 3 và N = 17 28 + 28 29 − 19 30 − 20 31 . − 5 12 + 1 4 + 1 6 . Khi đó tổng M + N bằng
A. − 62 125
B. 31 1000
C. − 31 100
D. 31 100
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\(\dfrac{17}{5}.\dfrac{-31}{125}.\dfrac{1}{2}.\dfrac{10}{17}.\dfrac{-1}{2^3}\\= \left(\dfrac{17}{5}.\dfrac{10}{17}\right)\left(\dfrac{-31}{125}.\dfrac{-1}{8}\right).\dfrac{1}{2}\\ =2.\dfrac{31}{1000}.\dfrac{1}{2}\\ =\left(2.\dfrac{1}{2}\right).\dfrac{31}{1000}\\ =1.\dfrac{31}{1000}\\ =\dfrac{31}{1000}\)
1) \(\dfrac{17}{5}\cdot\dfrac{-31}{125}\cdot\dfrac{1}{2}\cdot\dfrac{10}{17}\cdot\dfrac{-1}{2^3}\)
\(=\dfrac{17\cdot\left(-31\right)\cdot1\cdot2\cdot5\cdot\left(-1\right)}{5\cdot125\cdot2\cdot17\cdot8}\)
\(=\dfrac{\left(-31\right)\left(-1\right)}{125\cdot8}\\ =\dfrac{31}{1000}\)
b: D=(-3/31-28/31)+(-6/17-11/17)+(1/25-5/25)
=-2-4/25=-54/25
4: \(=\dfrac{2+3}{7}+\dfrac{1+6}{9}-\dfrac{5}{6}=\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{5}{6}=\dfrac{83}{126}\)
5: \(=\dfrac{-5-2}{7}+\dfrac{3+1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)
6: \(=\dfrac{-3-28}{31}+\dfrac{-6-1}{17}+\dfrac{1-5}{25}=-1-\dfrac{7}{17}-\dfrac{4}{25}=-\dfrac{668}{425}\)
4. \(\dfrac{2}{7}+\dfrac{1}{9}+\dfrac{3}{7}+\dfrac{5}{9}+\dfrac{-5}{6}\)
\(=\left(\dfrac{2}{7}+\dfrac{3}{7}\right)+\left(\dfrac{1}{9}+\dfrac{5}{9}\right)+\dfrac{-5}{6}\)
\(=\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{-5}{6}\)
\(=\dfrac{30+28+\left(-35\right)}{42}=\dfrac{23}{42}\)
5. \(\dfrac{-5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\)
\(=\left(\dfrac{-5}{7}+\dfrac{-2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\)
\(=\dfrac{-7}{7}+\dfrac{4}{4}+\dfrac{-1}{5}\)
\(=-1+1+\dfrac{-1}{5}\)
\(=-\dfrac{1}{5}\)
6. \(\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-1}{17}+\dfrac{-1}{5}\)
\(=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-1}{17}\right)+\dfrac{1}{25}+\dfrac{-1}{5}\)
\(=\dfrac{-31}{31}+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)
\(=-1+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)
\(=\dfrac{-425+\left(-175\right)+17+\left(-85\right)}{425}=\dfrac{-668}{425}\)
a: \(=\dfrac{-5}{7}-\dfrac{2}{7}+\dfrac{3}{4}+\dfrac{1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)
b: \(=\dfrac{-3}{31}-\dfrac{28}{31}+\dfrac{-6}{17}-\dfrac{11}{17}+\dfrac{1}{29}-\dfrac{1}{5}=\dfrac{-24}{145}\)
A = - \(\dfrac{3}{31}\) - \(\dfrac{6}{17}\) + \(\dfrac{1}{2}\) - \(\dfrac{28}{31}\) - \(\dfrac{11}{17}\)- \(\dfrac{1}{6}\)
A = -( \(\dfrac{3}{31}\) + \(\dfrac{28}{31}\)) - ( \(\dfrac{6}{17}\) + \(\dfrac{11}{17}\)) +( \(\dfrac{1}{2}\)- \(\dfrac{1}{6}\))
A = - \(\dfrac{31}{31}\) - \(\dfrac{17}{17}\)+ \(\dfrac{1}{3}\)
A = -1 - 1 + \(\dfrac{1}{3}\)
A = \(-\dfrac{5}{3}\)
Đáp án cần chọn là: B
M = 17 5 . − 31 125 . 1 2 . 10 17 . − 1 2 3 M = 17. − 31 .1.10. − 1 3 5.125.2.17.2 3 M = − 31. − 1 125.2 3 M = 31 1000
N = 17 28 + 28 29 − 19 30 − 20 31 . − 5 12 + 1 4 + 1 6 N = 17 28 + 28 29 − 19 30 − 20 31 . − 5 12 + 3 12 + 2 12 N = 17 28 + 28 29 − 19 30 − 20 31 .0 N = 0
Vậy M + N = 31 1000 + 0 = 31 1000