Question

a) \(\dfrac{-1}{2}+\dfrac{1}{3}+\dfrac{5}{6}\)

b) \(\dfrac{-3}{8}+\dfrac{7}{4}-\dfrac{1}{12}\)

c) \(\dfrac{-5}{7}-\dfrac{3}{8}+\dfrac{1}{28}\)

d) Tính giá trị biểu thức

A= \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+......+\dfrac{2}{97.99}\)

Answer 1

`a)[-1]/2+1/3+5/6=[-3]/6+2/6+5/6=[-3+2+5]/6=4/6=2/3`

`b)[-3]/8+7/4-1/12=[-9]/24+42/24-2/24=[-9+42-2]/24=31/24`

`c)[-5]/7-3/8+1/28=[-40]/56-21/56+2/56=[-40-21+2]/56=[-59]/56`

`d)A=2/[1.3]+2/[3.5]+2/[5.7]+...+2/[97.99]`

   `A=1-1/3+1/3-1/5+1/5-1/7+...+1/97-1/99`

   `A=1-1/99`

   `A=99/99-1/99=98/99`

Answer 2

\(a,-\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{5}{6}=-\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{5}{6}=\dfrac{\left(-3\right)+2+5}{6}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(b,-\dfrac{3}{8}+\dfrac{7}{4}-\dfrac{1}{12}=-\dfrac{9}{24}+\dfrac{42}{24}-\dfrac{2}{24}=\dfrac{\left(-9\right)+42-2}{24}=\dfrac{31}{24}\)

\(c,-\dfrac{5}{7}-\dfrac{3}{8}+\dfrac{1}{28}=-\dfrac{40}{56}-\dfrac{21}{56}+\dfrac{2}{56}=\dfrac{\left(-40\right)-21+2}{56}=\dfrac{-59}{56}\)

\(d,\) Tính giá trị biểu thức

\(A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\)

\(A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\)

\(A=1-\dfrac{1}{99}\)

\(A=\dfrac{99-1}{99}=\dfrac{98}{99}\)