题目内容
神机妙算细又巧!
(1)
÷
×
(2)(
+
)÷
(3)
×
+
÷4
(4)1836÷[56×(
-
)]
(5)
+
+…+
+
.
(1)
2 |
9 |
8 |
27 |
2 |
15 |
(2)(
1 |
4 |
3 |
10 |
3 |
4 |
(3)
5 |
6 |
1 |
4 |
1 |
6 |
(4)1836÷[56×(
4 |
7 |
1 |
4 |
(5)
1 |
1×2 |
1 |
2×3 |
1 |
98×99 |
1 |
99×100 |
分析:(1)
÷
×
,把除法改为乘法后,分子与分母互相约分;
(2)(
+
)÷
,运用除法的运算性质(a+b)÷c=a÷c+b÷c简算;
(3)
×
+
÷4,把除以4改为乘
,然后用乘法分配律的逆运算简算;
(4)1836÷[56×(
-
)],中括号内内运用乘法分配律简算;
(5)
+
+…+
+
,利用
=
-
简算.
2 |
9 |
8 |
27 |
2 |
15 |
(2)(
1 |
4 |
3 |
10 |
3 |
4 |
(3)
5 |
6 |
1 |
4 |
1 |
6 |
1 |
4 |
(4)1836÷[56×(
4 |
7 |
1 |
4 |
(5)
1 |
1×2 |
1 |
2×3 |
1 |
98×99 |
1 |
99×100 |
1 |
n(n+1) |
1 |
n |
1 |
n+1 |
解答:解:(1)
÷
×
,
=
×
×
,
=
;
(2)(
+
)÷
,
=
÷
+
÷
,
=
×
+
×
,
=
+
,
=
+
,
=
;
(3)
×
+
÷4,
=
×
+
×
,
=(
+
)×
,
=1×
,
=
;
(4)1836÷[56×(
-
)],
=1836÷[56×
-56×
],
=1836÷[32-14],
=1836÷18,
=102;
(5)
+
+…+
+
,
=(
-
)+(
-
)+…+(
-
)+(
-
),
=1-
,
=
.
2 |
9 |
8 |
27 |
2 |
15 |
=
2 |
9 |
27 |
8 |
2 |
15 |
=
1 |
10 |
(2)(
1 |
4 |
3 |
10 |
3 |
4 |
=
1 |
4 |
3 |
4 |
3 |
10 |
3 |
4 |
=
1 |
4 |
4 |
3 |
3 |
10 |
4 |
3 |
=
1 |
3 |
2 |
5 |
=
5 |
15 |
6 |
15 |
=
11 |
15 |
(3)
5 |
6 |
1 |
4 |
1 |
6 |
=
5 |
6 |
1 |
4 |
1 |
6 |
1 |
4 |
=(
5 |
6 |
1 |
6 |
1 |
4 |
=1×
1 |
4 |
=
1 |
4 |
(4)1836÷[56×(
4 |
7 |
1 |
4 |
=1836÷[56×
4 |
7 |
1 |
4 |
=1836÷[32-14],
=1836÷18,
=102;
(5)
1 |
1×2 |
1 |
2×3 |
1 |
98×99 |
1 |
99×100 |
=(
1 |
1 |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
98 |
1 |
99 |
1 |
99 |
1 |
100 |
=1-
1 |
100 |
=
99 |
100 |
点评:此题考查了学生的运算技巧,因此在做此类题时,注意审题,寻求简便计算的方法,使计算过程简化.
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