Câu 1 : Thực hiện các phép tính sau bằng cách nhanh nhất :
a, 1996 + 3992 + 5988 + 7984
b, 2 . 3 . 4 . 8 . 50 . 25 . 125
c, ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( 45 . 128 - 90 . 64 ) . ( 1995 . 1996 + 1997 . 1998 )
d, 1998 . 1996 + 1997 . 11 + 1985
----------------------------------------------
1997 .1996 - 1995 . 1996
a, 1996 + 3992 + 5988 + 7984
= ( 1996 + 7984 ) + ( 3992 + 5988 )
= 9980 + 9980
= 19 960
b, 2 . 3 . 4 . 8 . 50 . 25 . 125
= ( 2 .50 ) . ( 4 . 25 ) . ( 8 . 125 ) . 3
= 100 . 100 . 1000 . 3
= 10 000 . 1000 . 3
= 10 000 000 . 3
= 30 000 000
c, ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( 45 . 128 - 90 . 64 ) . ( 1995 . 1996 + 1997 . 1998 )
= ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( ( 45 . 2 ) . ( 128 : 2 ) - 90 . 64 ) . ( 1995 . 1996 + 1997 . 1998 )
= ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( 90 . 64 - 90 . 64 ) . ( 1995 . 1996 + 1997 . 1998 )
= ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( ( 90 - 90 ) - ( 64 - 64 ) . ( 1995 . 1996 + 1997 . 1998 )
= ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . ( 0 - 0 ) . ( 1995 . 1996 + 1997 . 1998 )
= ( 45 . 46 + 47 . 48 ) . ( 51 . 52 - 49 . 48 ) . 0 . ( 1995 . 1996 + 1997 . 1998 )
Vậy số đó là 0
d, 1998 . 1996 + 1997 . 11 + 1985
----------------------------------------------
1997 .1996 - 1995 . 1996
1998 . 1996 + (1996 + 1) . 10 + 11 + 1985
= ----------------------------------------------------------
1996 . (1997 - 1995)
1998 . 1996 + 1996 . 10 + 1996 + 10
= ---------------------------------------------------
1996 . 2
1996 . (10 + 1 + 1998) + 10
= ---------------------------------------------------
1996 . 2
1996 . 2009 + 10
= ---------------------------------------------------
1996 . 2
2009 + 10
= --------------------------------------------------- (Chia cả hai vế cho 1996)
2
2019
= ---------------------------------------------------
2
Vậy số đó là 1009,5