Question

1. Tính nhanh
a) A= -2/5 + 3/-4 + 6/7 + 3/4 + 2/5
b) B= -1/8 + 7/9 + 7/-8 + 6/7 + 2/14
c) A= 2/3 +1/5. 10/7
d) B=7/12 -27/7 . 1/18
e) 4/9 . 13/3 - 4/3 . 40/9
f) cho M= 1/3.5 + 1/5.7 + 1/7.9 + ... + 1/97.99
 giúp mik với được ko? :(( 

Answer 1

a: A=-2/5+2/5+3/4-3/4+6/7=6/7

b: A=-1/8-7/8+7/9+6/7+1/7

=7/9

c: A=2/3+2/7=20/21

e: \(=\dfrac{4\cdot13-4\cdot40}{3\cdot9}=\dfrac{4\cdot\left(-27\right)}{-27}=-4\)

Answer 2

`A = -2/5 + 3/(-4) + 6/7 + 3/4 + 2/5`

`A=  (-2/5+2/5)+(3/(-4) + 3/4) + 6/7`

`A = 0+0+6/7`

`A=6/7`

________________________

`B=-1/8 + 7/9 + 7/(-8) + 6/7 + 2/14`

`B = (-1/8 + 7/(-8)) + (6/7 + 2/14) + 7/9`

`B = -1 + 1 + 7/9`

`B = 0+ 7/9`

`B  =7/9`

_________________________________________

`A = 2/3 + 1/5 . 10/7`

`A = 2/3 + (1xx10)/(5xx7)`

`A = 2/3 + 57/35`

`A= 241/105`

___________________________

`B = 7/12 - 27/7 . 1/18`

`B = 7/12 - (27.1)/(7.18)`

`B=7/12- 3/14`

`B= 31/84`

__________________________

`4/9 . 13/3 - 4/3 . 40/9`

`=(4.13)/(9.3) - (4.40)/(3.9)`

`=(4.13-4.40)/(9.3)`

`=(4.(13-40))/27`

`=(4.(-27))/27`

`=-4`

____________________________________

`M=1/(3.5) + 1/(5.7) + 1/(7.9) + .... +1/(97.99)`

`M = 1/2 . (2/(3.5) + 2/(5.7) + 2/(7.9) + .... +2/(97.99))`

`M = 1/2 . (1/3 - 1/5 + 1/5 - 1/7 + ...... + 1/97 - 1/99)`

`M = 1/2 . (1/3 - 1/99)`

`M = 1/2 . 32/99`

`M= 16/99`

Answer 3

a/\(A=\left(-\dfrac{2}{5}+\dfrac{2}{5}\right)+\left(\dfrac{3}{-4}+\dfrac{3}{4}\right)+\dfrac{6}{7}=0+0+\dfrac{6}{7}=\dfrac{6}{7}\)

b/ \(B=\left(\dfrac{-1}{8}+\dfrac{7}{-8}\right)+\dfrac{7}{9}+\left(\dfrac{6}{7}+\dfrac{2}{14}\right)=\left(-\dfrac{1}{8}+\dfrac{-7}{8}\right)+\dfrac{7}{9}+\left(\dfrac{6}{7}+\dfrac{1}{7}\right)\\ =-1+\dfrac{7}{9}+1=0+\dfrac{7}{9}=\dfrac{7}{9}\)

c/

\(A=\dfrac{2}{3}+\dfrac{1.10}{5.7}=\dfrac{2}{3}+\dfrac{1.5.2}{5.7}=\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{20}{21}\)

D/

\(B=\dfrac{7}{12}-\dfrac{27.1}{7.18}=\dfrac{7}{12}-\dfrac{9.3.1}{7.2.9}=\dfrac{7}{12}-\dfrac{3}{14}=\dfrac{31}{84}\)

E/

\(=\dfrac{4}{9}.\dfrac{13}{3}-\dfrac{4}{9}.\dfrac{40}{3}=\dfrac{4}{9}.\left(\dfrac{13}{3}-\dfrac{40}{3}\right)=\dfrac{4}{9}.\left(-\dfrac{27}{3}\right)=\dfrac{4}{9}.\left(-9\right)=-4\)

F/

\(\Rightarrow2M=2\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\right)\)

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

\(2M=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\\ 2M=\dfrac{1}{3}-\dfrac{1}{99}=\dfrac{32}{99}\)

\(\Rightarrow M=\dfrac{32}{99}:2=\dfrac{16}{99}\)