题目内容
计算:
①2
-1.75=
;②30
×
=
③(
+
+
)÷
=
④30×29-29×28+28×27-27×26+…+4×3-3×2=
⑤1÷(1-
)×(1+
)÷(1-
)×(1+
)÷…÷(1-
)×(1+
)=
;
⑥方程:65%(x-1)=37%(x+1)+0.1的解是x=
①2
1 |
3 |
7 |
12 |
7 |
12 |
1 |
28 |
1 |
29 |
1
1 |
28 |
1
;1 |
28 |
③(
1 |
7×8 |
1 |
8×9 |
1 |
9×10 |
1 |
7×8×9 |
21.6
21.6
;④30×29-29×28+28×27-27×26+…+4×3-3×2=
448
448
.⑤1÷(1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
10 |
1 |
10 |
121 |
2 |
121 |
2 |
⑥方程:65%(x-1)=37%(x+1)+0.1的解是x=
4
4
.分析:①先把小数化成分数再计算;
②30
分解成29+
,再运用乘法分配律简算;
③先把除法变成乘法,再运用乘法分配律简算;
④30×29-29×28结合在一起,然后使用乘法分配律简算;28×27-27×26结合在一起,然后使用乘法分配律简算;4×3-3×2结合在一起使用乘法分配律简算;
⑤把括号里面的运算算出,然后把除法变成乘法,再约分求解;
⑥先运用乘法分配律把等号左后的括号去掉,再根据等式的性质解方程.
②30
1 |
28 |
29 |
28 |
③先把除法变成乘法,再运用乘法分配律简算;
④30×29-29×28结合在一起,然后使用乘法分配律简算;28×27-27×26结合在一起,然后使用乘法分配律简算;4×3-3×2结合在一起使用乘法分配律简算;
⑤把括号里面的运算算出,然后把除法变成乘法,再约分求解;
⑥先运用乘法分配律把等号左后的括号去掉,再根据等式的性质解方程.
解答:解:①2
-1.75,
=2
-1
,
=
;
②30
×
,
=(29+
)×
,
=29×
+
×
,
=1+
,
=1
;
③(
+
+
)÷
,
=(
+
+
)×(7×8×9),
=
×(7×8×9)+
×(7×8×9)+
×(7×8×9),
=9+7+5.6,
=21.6;
④30×29-29×28+28×27-27×26+…+4×3-3×2,
=(30-28)×29+(28-26)×27+…+(4-2)×3,
=2×29+2×27+…2×3,
=2×(29+27+25+…+3),
=2×[(3+29)×14÷2],
=2×[32×14÷2],
=2×448÷2,
=448;
⑤1÷(1-
)×(1+
)÷(1-
)×(1+
)÷…÷(1-
)×(1+
),
=1÷
×
÷
×
÷…÷
×
,
=1×2×
×
×
×
×…×
×
×
,
=1×2×
×
×1×1×…×1×11×11,
=
×121,
=
;
⑥65%(x-1)=37%(x+1)+0.1,
65%x-65%=37%x+37%+0.1,
0.65x-0.65=0.37x+0.47,
0.65x-0.65+0.65=0.37x+0.47+0.65,
0.65x=0.37x+1.12,
0.65x-0.37x=0.37x+1.12-0.37x,
0.28x=1.12,
0.28x÷0.28=1.12÷0.28,
x=4.
1 |
3 |
=2
1 |
3 |
3 |
4 |
=
7 |
12 |
②30
1 |
28 |
1 |
29 |
=(29+
29 |
28 |
1 |
29 |
=29×
1 |
29 |
29 |
28 |
1 |
29 |
=1+
1 |
28 |
=1
1 |
28 |
③(
1 |
7×8 |
1 |
8×9 |
1 |
9×10 |
1 |
7×8×9 |
=(
1 |
7×8 |
1 |
8×9 |
1 |
9×10 |
=
1 |
7×8 |
1 |
8×9 |
1 |
9×10 |
=9+7+5.6,
=21.6;
④30×29-29×28+28×27-27×26+…+4×3-3×2,
=(30-28)×29+(28-26)×27+…+(4-2)×3,
=2×29+2×27+…2×3,
=2×(29+27+25+…+3),
=2×[(3+29)×14÷2],
=2×[32×14÷2],
=2×448÷2,
=448;
⑤1÷(1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
10 |
1 |
10 |
=1÷
1 |
2 |
3 |
2 |
2 |
3 |
4 |
3 |
9 |
10 |
11 |
10 |
=1×2×
3 |
2 |
3 |
2 |
4 |
3 |
4 |
3 |
10 |
9 |
11 |
10 |
11 |
10 |
=1×2×
1 |
2 |
1 |
2 |
=
1 |
2 |
=
121 |
2 |
⑥65%(x-1)=37%(x+1)+0.1,
65%x-65%=37%x+37%+0.1,
0.65x-0.65=0.37x+0.47,
0.65x-0.65+0.65=0.37x+0.47+0.65,
0.65x=0.37x+1.12,
0.65x-0.37x=0.37x+1.12-0.37x,
0.28x=1.12,
0.28x÷0.28=1.12÷0.28,
x=4.
点评:本题主要考查了较复杂的简便运算的方法,特别是对乘法分配律的使用要能灵活运用.
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