①5.75-8.63+(9.25-2.37)
②15.7-8
-2
③(44×4)×25
④999×363+7364
⑤9.8+99.8+999.8+9999.8+99999.8
⑥1-
+
+
+
⑦(1+
+
+
)×(
+
+
+
)-(1+
+
+
+
)×(
+
+
)⑧
×48.解:①5.75-8.63+(9.25-2.37),=5.75-8.63+9.25-2.37,
=(5.75+9.25)-(8.63+2.37),
=15-11,
=4;
②15.7-8
-2
,=15.7-(8
+2
),=15.7-11,
=4.7;
③(44×4)×25,
=44×(4×25),
=44×100,
=4400;
④999×363+7364,
=(1000-1)×363+7364,
=1000×363-1×363+7346,
=363000-363+7364,
=363000+(7364-363),
=363000+7001,
=370001;
⑤9.8+99.8+999.8+9999.8+99999.8,
=(10-0.2)+(100-0.2)+(1000-0.2)+(10000-0.2)+(100000-0.2),
=(10+100+1000+10000+100000)-(0.2+0.2+0.2+0.2+0.2),
=111110-(0.2×5),
=111110-1,
=111109;
⑥1-
+
+
+
,=1-
+(
-
)+(
-
)+(
-
),=1-
+
-
+
-
+
-
,=1-
,=
;⑦令
+
+
=a,那么:(1+
+
+
)×(
+
+
+
)-(1+
+
+
+
)×(
+
+
),=(1+a)×(a+
)-(1+a+
)×a,=(a+
+a2+
a)-(1
+a)×a,=(
+1
a+a2)-(1
a+a2),=
+1
a+a2-1
a-a2,=
+(1
a-1
a)+(a2-a2),=
+0+0,=
;⑧
×48,=(1-
)×48,=1×48-
×48,=48-
,=47
.分析:①运用加法交换律和结合律简算;
②根据减法的性质简算;
③运用乘法结合律简算;
④先把999分解成1000-1,再运用乘法分配律简算,然后再运用加法结合律简算;
⑤先把每个加数都分解成一个整数减去0.2,再运用加法结合律以及乘法的意义简算;
⑥根据
=
-
,
=
-
,
=
-
,化简求解;⑦令
+
+
=a,然后化简算式求解;⑧把
分解成1-
,再运用乘法分配律简算.点评:完成本题要注意分析式中数据,运用合适的简便方法计算.