93,85 - 34,15 - 12,49 - (3,85 - 2,49) - 5,85
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a: \(=41.54+8.46-3.18-5.82+23.17-3.17\)
=50-9+20
=70-9=61
b: \(=123.8-34.15-5.85-12.49+2.49+10\)
=123,8-40
=83,8
c: \(=32.18+36.42+13.93-2.18-6.42-3.93\)
=30+30+10
=70
a: \(A=\left(41.54+8.46\right)-\left(3.18+5.82\right)+\left(23.17-3.17\right)\)
=50-9+20
=70-9
=61
b: \(B=123.8-\left(34.15+5.84\right)+\left(-12.49+2.49\right)\)
\(=123.8-40-10=73.8\)
c: \(C=\left(32.18-2.18\right)+\left(36.42-6.42\right)+\left(13.93-3.93\right)\)
=30+30+10
=70
a: A=(41.54+8.46)−(3.18+5.82)+(23.17−3.17)A=(41.54+8.46)−(3.18+5.82)+(23.17−3.17)
=50-9+20
=70-9
=61
b: B=123.8−(34.15+5.84)+(−12.49+2.49)B=123.8−(34.15+5.84)+(−12.49+2.49)
=123.8−40−10=73.8=123.8−40−10=73.8
c: C=(32.18−2.18)+(36.42−6.42)+(13.93−3.93)C=(32.18−2.18)+(36.42−6.42)+(13.93−3.93)
=30+30+10
=70
B = 123,8 - 34,15 - 12,49 - (5,85 - 2,49) + 10,2
B= 123,8 - 34,15 -12,49 - 3,36 + 10,2
B= 84
\(I=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2009.2010}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2019}-\dfrac{1}{2010}\\ =1-\dfrac{1}{2010}\\ =\dfrac{2009}{2010}\)
\(K=\dfrac{4}{2.4}+\dfrac{4}{4.6}+...+\dfrac{4}{2008.2010}\\ =2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{2008.2010}\right)\\ =2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\\ =2\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\\ =2.\dfrac{502}{1005}\\ =\dfrac{1004}{1005}\)
\(F=\dfrac{1}{18}+\dfrac{1}{54}+...+\dfrac{1}{990}\\ =\dfrac{1}{3.6}+\dfrac{1}{6.9}+...+\dfrac{1}{30.33}\\ =\dfrac{1}{3}\left(\dfrac{3}{3.6}+\dfrac{3}{6.9}+...+\dfrac{3}{30.33}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{30}-\dfrac{1}{33}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{33}\right)\\ =\dfrac{1}{3}.\dfrac{10}{33}\\ =\dfrac{10}{99}\)
\(I=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2009}-\dfrac{1}{2010}=\dfrac{2010-1}{2010}=\dfrac{2008}{2010}\)
\(K=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}=\dfrac{502}{1005}\)
\(F=\dfrac{1}{3.6}+\dfrac{1}{6.9}+...+\dfrac{1}{99.100}=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{100}\right)=\dfrac{97}{900}\)
\(a,2+\dfrac{2}{3}=\dfrac{6}{3}+\dfrac{2}{3}=\dfrac{8}{3}\\ \dfrac{6}{9}-\dfrac{6}{11}=\dfrac{66}{99}-\dfrac{54}{99}=\dfrac{12}{99}=\dfrac{4}{33}\\ b,21\times\dfrac{4}{7}=12\\ \dfrac{54}{30}:\dfrac{6}{5}=\dfrac{9}{5}\times\dfrac{5}{6}=\dfrac{3}{2}\)
\(y:\dfrac{3}{11}=\dfrac{7}{6}+\dfrac{2}{3}\)
\(y:\dfrac{3}{11}=\dfrac{11}{6}\)
\(y=\dfrac{11}{6}\times\dfrac{3}{11}\)
\(y=\dfrac{1}{2}\)
Bài 3
\(\dfrac{3}{7}:\dfrac{1}{4}-\dfrac{1}{2}=\dfrac{3}{7}\times\dfrac{4}{1}-\dfrac{1}{2}=\dfrac{12}{7}-\dfrac{1}{2}=\dfrac{24}{14}-\dfrac{7}{14}=\dfrac{17}{14}\)
`2)`
`y:3/11=7/6+2/3`
`y:3/11=11/6`
`y=11/6xx3/11`
`y=1/2`
`3)`
`=12/7-1/2=24/14-7/14=17/14`
`7/12 + 3/4 xx 2/9`
`= 7/12 + 1/6`
`= 9/12`
_________________
`8/9 - 4/15 : 2/5`
`= 8/9 - 2/3`
`= 2/9`
\(A=\dfrac{31\cdot\left(31^{12}-1\right)}{31\left(31^{13}+1\right)}=\dfrac{31^{13}+1-32}{31\left(31^{13}+1\right)}=\dfrac{1}{31}-\dfrac{32}{31^{14}+31}\)
\(B=\dfrac{31\left(31^{13}-1\right)}{31\left(31^{14}+1\right)}=\dfrac{1}{31}-\dfrac{32}{31^{15}+31}\)
Dễ thấy \(31^{14}+31< 31^{15}+31\Rightarrow\dfrac{32}{31^{14}+31}>\dfrac{32}{31^{15}+31}\\ \Rightarrow\dfrac{1}{31}-\dfrac{32}{31^{14}+31}< \dfrac{1}{31}-\dfrac{32}{31^{15}+31}\)
Vậy A < B
ngắn gọn mà đúng ý
93,85-34,15-12,49-(3,85-2,49)-5,85
=93,85-34,15-12,49-1,36-5,85
=40