7
9
×(4.85÷
5
18
-3.6+6.15×3
3
5
1998+1997×1999
1998×1999-1
1
3
+
1
15
+
1
35
+
1
63
+
1
99
+
1
143

20.07×39+200.7×4.1+40×10.035
2012-2011+2010-2009+2008-2007+…+4-3+2-1.
分析:(1)把除法改為乘法,括號內(nèi)運用乘法分配律簡算;
(2)把分子中的997看作1998-1,運用乘法分配律簡算,進過計算,發(fā)現(xiàn)分子與分母相同,因此.得數(shù)為;
(3)把每個分數(shù)的分母寫成兩個自然數(shù)相乘的形式,然后通過拆分,簡算即可;
(4)把原式變?yōu)?0.07×39+20.07×41+20.07×20,運用乘法分配律簡算;
(5)通過觀察,每兩個數(shù)分為一組,每組的結(jié)果為1,共分成2012÷2組,計算即可.
解答:解:(1)
7
9
×(4.85÷
5
18
-3.6+6.15×3
3
5
),
=
7
9
×(4.85×
18
5
-3.6+6.15×
18
5
),
=
7
9
×[(4.85-1+6.15)×
18
5
],
=
7
9
×[10×
18
5
],
=
7
9
×36,
=28;

(2)
1998+1997×1999
1998×1999-1
,
=
1998+(1998-1)×1999
1998×1999-1

=
1998+1998×1999-1999
1998×1999-1
,
=
1998×1999-1
1998×1999-1

=1;

(3)
1
3
+
1
15
+
1
35
+
1
63
+
1
99
+
1
143

=
1
1×3
+
1
3×5
+
1
5×7
+
1
7×9
+
1
9×11
+
1
11×13
,
=
1
2
×[(1-
1
3
)+(
1
3
-
1
5
)+(
1
5
-
1
7
)+(
1
7
-
1
9
)+(
1
9
-
1
11
)+(
1
11
-
1
13
)],
=
1
2
×[1-
1
13
],
=
1
2
×
12
13

=
6
13


(4)20.07×39+200.7×4.1+40×10.035,
=20.07×39+20.07×41+2×10.035×20,
=20.07×39+20.07×41+20.07×20,
=20.07×(39+41+20),
=20.07×100,
=2007;

(5)2012-2011+2010-2009+2008-2007+…+4-3+2-1,
=(2012-2011)+(2010-2009)+…+(2-1),
=1×(2012÷2),
=1006.
點評:完成此題,注意分析式中數(shù)據(jù),運用運算技巧和運算定律,靈活簡算.
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