Đáp án:

 `1000.`

Giải thích các bước giải:

Cách 1: tính thủ công.

 `{1978.2021+2022.21+2000}/{1980.2021-1978.2021}`

`= {2.23.43.43.47+2.3.337.3.7+2^4. 5^3}/{2^2 . 3^2 . 5. 11.43.47-2.23.43.43.47}`

`= {2.(23.43.43.47+ 3.337.3.7+ 2^3 . 5^3)}/{2.(2 . 3^2 . 5 . 11.43.47 - 23.43.43.47)}`

`= {23.43.43.47+ 3.337.3.7+ 2^3 . 5^3}/{2 . 3^2 . 5 . 11 .43.47- 23.43.43.47}`

`={1998769+ 21231+ 1000 }/ {2000790 - 1998769}`

`=2021000/2021=1000.`

Cách 2: ngắn gọn và hay hơn.

 `{1978.2021+2022.21+2000}/{1980.2021-1978.2021}`

` ={1978.2021+(2021+1).21+2000}/{2021(1980-1978)}`

` ={1978.2021+2021. 21 + 21+2000}/{2021(1980-1978)}`

` ={1978.2021+2021. 21 +2021}/{2021(1980-1978)}`

` ={2021.(1978+21+1)}/{2021.2}`

` ={2021.(1978+21+1)}/{2021.2}`

` ={2021.2000}/{2021.2}`

`=2000/2=1000.`

$\frac{1978 . 2021 + 2022 . 21 + 2000}{1980 . 2021 - 1978 . 2021}$ 

= $\frac{2021 . 1978 + ( 2021 + 1 ) . 21 + 2000}{2021 . ( 1980 - 1978 )}$ 

= $\frac{2021 . 1978 + 2021 . 21 + 21 + 2000}{2021 . 2}$ 

= $\frac{2021 . 1978 + 2021 . 21 + 2021 }{2021 . 2}$  

= $\frac{2021 . ( 1978 + 21 + 1 )}{2021 . 2}$   

=  $\frac{2021 . 2000}{2021 . 2}$   

= 1000