分析:(1)先算乘法再算除法,最后算减法;
(2)运用加法结合律简算;
(3)先把222×999变成666×333,然后再运用乘法分配律简算;
(4)先把小括号去掉(注意括号外是减法,里面的运算符合要改变),然后计算中括号里面的,最后算括号外的除法;
(5)
=1
-,
=
-,
=
-
…;
有以上规律化简求解;
(6)先把(289+
+
+
)÷(
+
+
)分成289÷(
+
+
)+(
+
+
)÷(
+
+
),然后在根据商不变规律简算.
解答:解:(1)2000-72×625÷36,
=2000-45000÷36,
=2000-1250,
=750;
(2)4.8-
+5.2-
,
=(4.8+5.2)-(
+
),
=10-1,
=9;
(3)222×999+333×334,
=666×333+333×334,
=(666+334)×333,
=1000×333,
=333000;
(4)[5
-(4.15-2
)]÷3
,
=[5
-4
+2
]÷3
,
=[1+2
]÷3
,
=3
÷3
,
=1;
(5)
+
+
+…+
,
=1-
+
-+
-
+…+
-
,
=1-
,
=
;
(6)(289+
+
+
)÷(
+
+
),
=289÷(
+
+
)+(
+
+
)÷(
+
+
),
=289÷(
+
+
)+1,
=(289×120)÷[120×(
+
+
)]+1,
=(289×120)÷[120×
+120×
+120×
]+1,
=(289×120)÷[100+105+84]+1,
=289×120÷289+1,
=289÷289×120+1,
=1×120+1,
=121.
点评:本题考查了较复杂的简便运算,注意找清楚规律,再根据规律化简.