Bài 4: Tính phân số a) 5/13. 7/9 + 5/9.9/13 - 5/9.3/13 b) 6/34 + (-2) + -15/33+ 14/17 + -6/11 c) 12 5/31 - ( 4 3/7 + 5 5/31) d) 1/2+ 1/2.3 + 1/3.4 + 1/4.5 + ....... + 1/2020.2021 + 1/2021.2022

a) $\dfrac{5}{13}$  .  $\dfrac{7}{9}$ + $\dfrac{5}{9}$  .  $\dfrac{9}{13}$ - $\dfrac{5}{9}$  .  $\dfrac{3}{13}$

= $\dfrac{5 . 7}{13 . 9}$   + $\dfrac{5}{9}$  .  $\dfrac{9}{13}$ - $\dfrac{5}{9}$  .  $\dfrac{3}{13}$

= $\dfrac{5}{9}$  .  $\dfrac{7}{13}$ + $\dfrac{5}{9}$  .  $\dfrac{9}{13}$ - $\dfrac{5}{9}$  .  $\dfrac{3}{13}$

= $\dfrac{5}{9}$  .  ( $\dfrac{7}{13}$ + $\dfrac{9}{13}$ - $\dfrac{3}{13}$ ) 

= $\dfrac{5}{9}$  .   $\dfrac{13}{13}$

= $\dfrac{5}{9}$  .  1 

= $\dfrac{5}{9}$  

b) `6/34` + `(-2)` + `(-15)/33` + `14/17` + `(-6)/11` 

= `6/34` + `(-2)` + `(-15)/33` + `28/34` + `(-18)/33` 

= ( `6/34` + `28/34` ) + ( `(-18)/33` + `(-15)/33` ) + `(-2 )` 

= `34/34` + `( -33)/33` + ( -2 ) 

= `1` + `( -1)` + `(-2 )` 

= `0` + `(-2 )` 

= `(-2 )` 

c) 12`5/31` - ( 4`3/7` + 5`5/31` )

= 12`5/31` -  4`3/7` - 5`5/31` 

= 12`5/31` -   5`5/31`  - 4`3/7`

= 7 - 4`3/7`

= 3 + 4 - 4 - `3/7` 

= 3 - `3/7` 

= `18/7` 

d) `1/2` + `1/( 2.3 )` + `1/( 3.4 )` + `1/( 4.5)` + ....... + `1/(2020.2021)` + `1/(2021.2022)`

= `1/(1.2)` + `1/( 2.3 )` + `1/( 3.4 )` + `1/( 4.5)` + ....... + `1/(2020.2021)` + `1/(2021.2022)`
= `1` - `1/2` + `1/2` - `1/3` + ...... + `1/2020` - `1/2021` + `1/2021` - `1/2022` 

= `1` - `1/2022` 

= `2021/2022`