题目内容
计算下列各题,能简便运算要使用简便计算
[7-(1
×
+1
×
)]÷1.75;
(2-
×
)÷(
+
);
+(
+
)×
;
÷[(
+
)×
];
2013-2012+2011-2010+…+3-2+1.
[7-(1
3 |
4 |
5 |
9 |
3 |
4 |
4 |
9 |
(2-
3 |
4 |
4 |
5 |
1 |
12 |
4 |
15 |
8 |
17 |
10 |
13 |
10 |
17 |
9 |
10 |
1 |
5 |
2 |
3 |
1 |
5 |
1 |
13 |
2013-2012+2011-2010+…+3-2+1.
考点:分数的四则混合运算,加减法中的巧算
专题:运算顺序及法则
分析:(1)先把小括号里的根据乘法分配律简算,然后再把中括号外边的除号变成乘号再利用乘法分配律简算;
(2)按照四则运算的计算方法,先算括号里的,再算括号外面的乘法;
(3)根据乘法的分配律和加法的交换律简算;
(4)先算小括号里的加法,再算小括号外面的乘法,最后算中括号外边的除法;
(5)从左向右每两项结合在一起,可得差为1,然后简算即可.
(2)按照四则运算的计算方法,先算括号里的,再算括号外面的乘法;
(3)根据乘法的分配律和加法的交换律简算;
(4)先算小括号里的加法,再算小括号外面的乘法,最后算中括号外边的除法;
(5)从左向右每两项结合在一起,可得差为1,然后简算即可.
解答:
解:(1)[7-(1
×
+1
×
)]÷1.75
=[7-(1
×(
+
)]÷1.75
=[7-1
]×
=7×
+
×
=4+1
=5
(2)(2-
×
)÷(
+
)
=(2-
)÷
=
×
=4
(3)
+(
+
)×
=
+
×
+
×
=
+
+
=
+
+
=1
(4)
÷[(
+
)×
]
=
÷[
×
]
=
÷
=3
(5)2013-2012+2011-2010+…+3-2+1
=(2013-2012)+(2011-2010)+…+(3-2)+1
=1×1006+1
=1007
3 |
4 |
5 |
9 |
3 |
4 |
4 |
9 |
=[7-(1
3 |
4 |
5 |
9 |
4 |
9 |
=[7-1
3 |
4 |
4 |
7 |
=7×
4 |
7 |
7 |
4 |
4 |
7 |
=4+1
=5
(2)(2-
3 |
4 |
4 |
5 |
1 |
12 |
4 |
15 |
=(2-
3 |
5 |
7 |
20 |
=
7 |
5 |
20 |
7 |
=4
(3)
8 |
17 |
10 |
13 |
10 |
17 |
9 |
10 |
=
8 |
17 |
10 |
13 |
9 |
10 |
10 |
17 |
9 |
10 |
=
8 |
17 |
9 |
13 |
9 |
17 |
=
8 |
17 |
9 |
17 |
9 |
13 |
=1
9 |
13 |
(4)
1 |
5 |
2 |
3 |
1 |
5 |
1 |
13 |
=
1 |
5 |
13 |
15 |
1 |
13 |
=
1 |
5 |
1 |
15 |
=3
(5)2013-2012+2011-2010+…+3-2+1
=(2013-2012)+(2011-2010)+…+(3-2)+1
=1×1006+1
=1007
点评:考查了运算定律与简便运算,四则混合运算.注意运算顺序和运算法则,灵活运用所学的运算律简便计算.
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