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\(\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+...+\frac{1}{9}.\frac{1}{10}\)
\(=\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{10}\)
\(=\frac{9}{10}\)
a) \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+........+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.........+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
b) \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+..........+\frac{2}{73.75}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{73}-\frac{1}{75}\)
\(=\frac{1}{3}-\frac{1}{75}=\frac{8}{25}\)
c) \(\frac{4}{4.6}+\frac{4}{6.8}+\frac{4}{8.10}+..........+\frac{4}{64.66}\)
\(=2.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+..........+\frac{2}{64.66}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+.....+\frac{1}{64}-\frac{1}{66}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{66}\right)=2.\frac{31}{132}=\frac{31}{66}\)
d) \(\frac{9}{5.8}+\frac{9}{8.11}+\frac{9}{11.14}+........+\frac{9}{497.500}\)
\(=3.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+..........+\frac{3}{497.500}\right)\)
\(=3.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+......+\frac{1}{497}-\frac{1}{500}\right)\)
\(=3.\left(\frac{1}{5}-\frac{1}{500}\right)=3.\frac{99}{500}=\frac{297}{500}\)
e) \(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+......+\frac{1}{93.95}\)
\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+........+\frac{2}{93.95}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+........+\frac{1}{93}-\frac{1}{95}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{95}\right)=\frac{1}{2}.\frac{18}{95}=\frac{9}{95}\)
g) \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+..........+\frac{1}{200.203}\)
\(=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+........+\frac{3}{200.203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+......+\frac{1}{200}-\frac{1}{203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{203}\right)=\frac{1}{3}.\frac{201}{406}=\frac{67}{406}\)
a) \(\dfrac{3}{8}+\dfrac{7}{12}+\dfrac{10}{16}+\dfrac{10}{24}\)
\(=\dfrac{3}{8}+\dfrac{7}{12}+\dfrac{5}{8}+\dfrac{5}{12}\)
\(=\left(\dfrac{3}{8}+\dfrac{5}{8}\right)+\left(\dfrac{7}{12}+\dfrac{5}{12}\right)\)
\(=1+1\)
\(=2\)
b) \(\dfrac{4}{6}+\dfrac{7}{13}+\dfrac{17}{9}+\dfrac{19}{13}+\dfrac{1}{9}+\dfrac{14}{6}\)
\(=\dfrac{2}{3}+\dfrac{7}{13}+\dfrac{17}{9}+\dfrac{19}{13}+\dfrac{1}{9}+\dfrac{7}{3}\)
\(=\left(\dfrac{2}{3}+\dfrac{7}{3}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)+\left(\dfrac{17}{9}+\dfrac{1}{9}\right)\)
\(=3+2+2\)
\(=7\)
c) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)
\(=1-\dfrac{1}{7}\)
\(=\dfrac{6}{7}\)
a, \(\frac{3}{5}-\left(-\frac{7}{10}\right)-\frac{13}{20}=\frac{3}{5}+\frac{7}{10}-\frac{13}{20}=\frac{12}{20}+\frac{14}{20}-\frac{13}{20}=\frac{13}{20}\)
b, \(\frac{3}{4}+\frac{-1}{3}-\frac{5}{18}=\frac{27}{36}+\frac{-12}{36}-\frac{10}{36}=\frac{5}{36}\)
c, \(\frac{3}{14}-\frac{5}{-8}+\frac{-1}{2}=\frac{12}{56}+\frac{35}{56}+\frac{-28}{56}=\frac{19}{56}\)
d, \(\frac{1}{2}+\frac{1}{-3}+\frac{1}{4}-\left(-\frac{1}{6}\right)=\frac{1}{2}+\frac{-1}{3}+\frac{1}{4}+\frac{1}{6}=\frac{6}{12}+\frac{-4}{12}+\frac{3}{12}+\frac{2}{12}=\frac{7}{12}\)
đ, \(\frac{19}{24}-\frac{1}{2}-\frac{1}{3}-\frac{7}{24}=\frac{19}{24}-\frac{12}{24}-\frac{8}{24}-\frac{7}{24}=-\frac{8}{24}=-\frac{1}{3}\)
g, \(-\frac{1}{3}+\frac{1}{2}-\frac{5}{6}=-\frac{2}{6}+\frac{3}{6}-\frac{5}{6}=-\frac{4}{6}=\frac{-2}{3}\)
e, \(\frac{4}{-9}+\frac{8}{5}+\frac{-5}{9}-\frac{2}{11}+\frac{7}{15}=\frac{-220}{495}+\frac{792}{495}+\frac{-275}{495}-\frac{90}{495}+\frac{231}{495}=\frac{438}{495}=\frac{146}{165}\)
ê, \(\frac{7}{11}-\left(\frac{3}{5}+\frac{7}{11}\right)=\frac{7}{11}-\frac{3}{5}-\frac{7}{11}=\left(\frac{7}{11}-\frac{7}{11}\right)-\frac{3}{5}=0-\frac{3}{5}=-\frac{3}{5}\)
Dài quá không nhanh được @@
1,
a,-3/5
b,-1/2
c,19/39
d,1/4
e,-39/40
f,-59/56
2,
a,=
b,<
c,>
d,<
k cho mình nha
\(A=\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+..........+\frac{1}{8}.\frac{1}{9}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{8.9}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.......+\frac{1}{8}-\frac{1}{9}=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)
\(B=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+....+\frac{1}{110}=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{10.11}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-.....+\frac{1}{10}-\frac{1}{11}=\frac{1}{4}-\frac{1}{11}=\frac{7}{44}\)
\(\text{c,d cơ bản tự làm nha }\)
A=>1.1/2.3+1.1/3.4+1.1/4.5+1.1/5.6+1.11/6.7+.1/7.8+1.1/8.9
=>1/2.3+1/3.4+1/4.5+1/6.7+1/7.8+1/8.9
=>1/2-1/3-1/4-1/5-1/6-1/7-1/8-1/9
=>1/2-1/9=>9/18-2/18=>7/18
Vậy A= 7/18
a) \(\dfrac{13}{20}+\dfrac{3}{5}+x=\dfrac{5}{6}\)
\(\Rightarrow\dfrac{5}{4}+x=\dfrac{5}{6}\)
\(\Rightarrow x=\dfrac{5}{6}-\dfrac{5}{4}\)
\(\Rightarrow x=\dfrac{-5}{12}\)
b) \(x+\dfrac{1}{3}=\dfrac{2}{5}-\dfrac{-1}{3}\)
\(\Rightarrow x+\dfrac{1}{3}=\dfrac{11}{15}\)
\(\Rightarrow x=\dfrac{11}{15}-\dfrac{1}{3}\)
\(\Rightarrow x=\dfrac{2}{5}\)
c)\(\dfrac{-5}{8}-x=\dfrac{-3}{20}-\dfrac{-1}{6}\)
\(\dfrac{-5}{8}-x=\dfrac{1}{60}\)
\(\Rightarrow x=\dfrac{-5}{8}-\dfrac{1}{60}\)
\(\Rightarrow x=\dfrac{-77}{120}\)
d) \(\dfrac{3}{5}-x=\dfrac{1}{4}+\dfrac{7}{10}\)
\(\Rightarrow\dfrac{3}{5}-x=\dfrac{19}{20}\)
\(\Rightarrow x=\dfrac{3}{5}-\dfrac{19}{20}\)
\(\Rightarrow x=\dfrac{-7}{20}\)
e) \(\dfrac{-3}{7}-x=\dfrac{4}{5}+\dfrac{-2}{3}\)
\(\Rightarrow\dfrac{-3}{7}-x=\dfrac{2}{15}\)
\(\Rightarrow x=\dfrac{-3}{7}-\dfrac{2}{15}\)
\(\Rightarrow x=\dfrac{-59}{105}\)
g) \(\dfrac{-5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)
\(\Rightarrow\dfrac{-5}{6}-x=\dfrac{1}{4}\)
\(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)
\(\Rightarrow x=\dfrac{-13}{12}\)
`#lv`
`-2/5+(-7/10)-9/6`
`=-2/5-7/10-9/6`
`=-4/10-7/10-9/6`
`=-11/10-3/2`
`=-11/10-15/10`
`=-26/10`
`=-13/5`
__
`1/2+(-2/5)-(-2/3)`
`=1/2-2/5+2/3`
`=5/10-4/10+2/3`
`=1/10+2/3`
`=3/30+20/30`
`=23/30`
__
`5/3-3/4+7/6`
`=20/12-9/12+14/12`
`=11/12+14/12`
`=25/12`
__
`-1/5+5/3-3/2`
`=-3/15+25/15-3/2`
`=22/15-3/2`
`=44/30-45/30`
`=-1/30`
__
`1/4-7/8+(-9/10)`
`=2/8-7/8-9/10`
`=-5/8-9/10`
`=-25/40-36/40`
`=-61/40`
__
`5/4+1/2+(-7/12)`
`=15/12+6/12-7/12`
`=21/12-7/12`
`=14/12`
`=7/6`
__
`-5/8-1/3+(-7/6)`
`=-5/8-1/3-7/6`
`=-15/24-8/24-28/24`
`=-52/24`
`=-13/6`
__
`-3/4-7/10+(-5/6)`
`=-3/4-7/10-5/6`
`=-45/60-42/60-50/60`
`=-137/60`
Bài làm
a, (-2/5) + (-7/10) - 9/6 =(-12/30) + (-21/30) - 45/30=(-33/30) - 45/30 = (-78/30)
b,1/2 + (-2/5) - (-2/3) = 15/30 + (-12/30) - (-20/30) = 3/30 - (-20/30) = 23/30
c,5/3 - 3/4 + 7/6 = 40/24 - 18/24 + 28/24 = 22/24 + 28/24 = 50/24 = 25/12
d, (-1/5) + 5/3 - 3/2 = (-6/30) + 50/30 - 45/30 = 44/30 - 45/30 = (-1/30)
e, 1/4 - 7/8 + (-9/10) = 10/40 - 35/40 - 36/40 = (-25/40) - 36/40 = (-61/40)
f, 5/4 +1/2 + (-7/12) = 15/12 + 6/12 - 7/12 = 21/12 - 7/12 = 14/12 = 7/6
g,(-5/8) -1/3 + (-7/6) = (-15/24) - 8/24 - 28/24 = (-23/24) - 28/24 = (-51/24)
k,(-3/4) - 7/10 + (-5/6) = (-45/60) - 42/60 - 50/60 = (-87/60) - 50/60 = (-137/60)
chúc bn học tốt nha
sai thì mn góp ý giúp mk
Đề bài là gì thế tinh hay là tính nhanh mk giúp cho
đó là tính thôi bạn làm kiểu gì cũng được