谁字怎么组词:五年级奥数专题解析;小数四则混合运算简算
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五年级奥数专题解析;小数四则混合运算简算
例题】
例1 用简便方法计算下面各题.
(1)(4.8×7.5×8.1)÷(2.4×2.5×2.7)
(2)0.125×0.25×0.5×64
(3)3.75×4.8+62.5×0.48
(4)1.35×0.61-0.35×0.61
解:(1)解法一:
(4.8×7.5×8.1)÷(2.4×2.5×2.7)
=(48×75×81)÷(24×25×27)
=(12×4×25×3×81)÷(6×4×25×3×9)
=(12×100×3×81)÷(6×100×3×9)
=(12×81)÷(6×9)
=(2×6×9×9)÷(6×9)
=2×9=18
从(48×75×81)÷(24×25×27)中可以看出:48是24的2倍,75是25的3倍,81是27的3倍,所以可以直接利用运算性质简算.
解法二:
(4.8×7.5×8.1)÷(2.4×2.5×2.7)
=(4.8÷2.4)×(7.5÷2.5)×(8.1÷2.7)
=2×3×3=18
(2)解法一:
0.125×0.25×0.5×64
=0.125×0.25×0.5×(2×4×8)
=(0.125×8)×(0.25×4)×(0.5×2)
=1×1×1=1
解法二:
0.125×0.25×0.5×64
=0.125×(0.25×0.5)×(8×8)
=(0.125×8)×(0.125×8)
=1×1=1
解法三:
0.125×0.25×0.5×64
=(64×0.5)×0.25×0.125
=32×(0.5×0.5)×(0.5×0.5×0.5)
=(32×0.5)×0.5×0.5×0.5×0.5
=(16×0.5)×0.5×0.5×0.5
=(8×0.5)×0.5×0.5
=(4×0.5)×0.5
=2×0.5=1
通过第(2)题三种算法,你认为哪一种最简便?你还有没有其它的简便解法?
(3)解法一:
3.75×4.8+62.5×0.48
= 37.5×0.48+62.5×0.48
=(37.5+62.5)×0.48
=100×0.48=48
解法二:
3.75×4.8+62.5×0.48
=3.75×4.8+6.25×4.8
=(3.75+6.25)×4.8
=10×4.8=48
(4)1.35×0.61-0.35×0.61
=(1.35-0.35)×0.61
=1×0.61
=0.61
例2 看一看下面的算式有什么特点?运用什么运算定律可以使计算简便?
(1)1.56×1.7+0.44×1.7-0.7
(2)11.72-7.85-(2.26+0.46)
解:(1)1.56×1.7+0.44×1.7-0.7
=1.7×(1.56+0.44)-0.7
=1.7×2-0.7
=3.4-0.7
=2.7
(2)11.72-7.85-(2.26+0.46)
=11.72-7.85-2.72
=11.72-2.72-7.85
=9-7.85
=1.15
例3 计算:0.1+0.3+0.5+0.7+…+0.97+0.99
分析:从0.1到0.9,前后两个数相差0.2,从0.11到0.99前后两个数相差0.02.
解:0.1+0.3+0.5+0.7+…+0.97+0.99
=(0.1+0.3+0.5+0.7+0.9)+(0.11+0.13+…
+0.19)+(0.21+0.23+…+0.29)+…+(0.91
+0.93+…+0.99)
=2.5+(0.1×5+0.25)+(0.25×5+0.25)+…
+(0.9×5+0.25)
=2.5+(0.1+0.2+…+0.9)×5+0.25×9
=2.5+22.5+2.25=27.25
【练习】
5.口算下面各题,并把它们得数熟记.
1.5×4 2.5×8 1÷0.125
0.25×0.4 0.8×1.25 1.4×0.5
5×0.2 0.06×1.5
6.用简便方法计算下面各题.
(1)5.5×17.3+6.7×5.5 (2)13.7×0.25×8
(3)32.8+5.6+7.2 (4)4.6×2.5×40
(5)12.5×3×3×8 (6)50×0.47×0.2
(7)101×7.3 (8)10.1×54
(9)42.6-2.77-7.23 (10)16.4-16.4×0.5
(11)2.18+4.65+7.82+4.35
(12)12.48-2.72-3.28
(13)(250+2.5)×4
(14)4×7×0.5×3×5
(15)(125+1.25)×8
(16)775+10.9+9.1+225
(17)12.4-2.68-7.32
(18)7×1.785+3×1.785
(19)5.25÷15+3.75÷15
(20)18.4×1.7+18.4×8.3
(21)7.6×5.3+7.6×3.7+7.6
(22)45.6÷38-7.6÷38
(23)(0.45+0.06+1.5)÷0.15
(24)2.75÷54+2.65÷54
(25)1.25×8.8 (26)0.89×10.1
(27)25×5.26×40 (28)0.125×32×25
(29)0.36×0.5+0.36×0.4+0.36×0.1
(30)0.38+13.4+1.62+4.6
(31)0.125×78×80
(32)9.1×1.1-9.1×0.1
(33)0.125×32×25×58
※(34)1.86×1.3+1.86×5.7+1.86×2+1.86
(35)79×0.99+21.79例题】 例1 用简便方法计算下面各题. (1)(4.8×7.5×8.1)÷(2.4×2.5×2.7) (2)0.125×0.25×0.5×64 (3)3.75×4.8+62.5×0.48 (4)1.35×0.61-0.35×0.61 解:(1)解法一: (4.8×7.5×8.1)÷(2.4×2.5×2.7) =(48×75×81)÷(24×25×27) =(12×4×25×3×81)÷(6×4×25×3×9) =(12×100×3×81)÷(6×100×3×9) =(12×81)÷(6×9) =(2×6×9×9)÷(6×9) =2×9=18 从(48×75×81)÷(24×25×27)中可以看出:48是24的2倍,75是25的3倍,81是27的3倍,所以可以直接利用运算性质简算. 解法二: (4.8×7.5×8.1)÷(2.4×2.5×2.7) =(4.8÷2.4)×(7.5÷2.5)×(8.1÷2.7) =2×3×3=18 (2)解法一: 0.125×0.25×0.5×64 =0.125×0.25×0.5×(2×4×8) =(0.125×8)×(0.25×4)×(0.5×2) =1×1×1=1 解法二: 0.125×0.25×0.5×64 =0.125×(0.25×0.5)×(8×8) =(0.125×8)×(0.125×8) =1×1=1 解法三: 0.125×0.25×0.5×64 =(64×0.5)×0.25×0.125 =32×(0.5×0.5)×(0.5×0.5×0.5) =(32×0.5)×0.5×0.5×0.5×0.5 =(16×0.5)×0.5×0.5×0.5 =(8×0.5)×0.5×0.5 =(4×0.5)×0.5 =2×0.5=1 通过第(2)题三种算法,你认为哪一种最简便?你还有没有其它的简便解法? (3)解法一: 3.75×4.8+62.5×0.48 = 37.5×0.48+62.5×0.48 =(37.5+62.5)×0.48 =100×0.48=48 解法二: 3.75×4.8+62.5×0.48 =3.75×4.8+6.25×4.8 =(3.75+6.25)×4.8 =10×4.8=48 (4)1.35×0.61-0.35×0.61 =(1.35-0.35)×0.61 =1×0.61 =0.61 例2 看一看下面的算式有什么特点?运用什么运算定律可以使计算简便? (1)1.56×1.7+0.44×1.7-0.7 (2)11.72-7.85-(2.26+0.46) 解:(1)1.56×1.7+0.44×1.7-0.7 =1.7×(1.56+0.44)-0.7 =1.7×2-0.7 =3.4-0.7 =2.7 (2)11.72-7.85-(2.26+0.46) =11.72-7.85-2.72 =11.72-2.72-7.85 =9-7.85 =1.15 例3 计算:0.1+0.3+0.5+0.7+…+0.97+0.99 分析:从0.1到0.9,前后两个数相差0.2,从0.11到0.99前后两个数相差0.02. 解:0.1+0.3+0.5+0.7+…+0.97+0.99 =(0.1+0.3+0.5+0.7+0.9)+(0.11+0.13+… +0.19)+(0.21+0.23+…+0.29)+…+(0.91 +0.93+…+0.99) =2.5+(0.1×5+0.25)+(0.25×5+0.25)+… +(0.9×5+0.25) =2.5+(0.1+0.2+…+0.9)×5+0.25×9 =2.5+22.5+2.25=27.25 【练习】 5.口算下面各题,并把它们得数熟记. 1.5×4 2.5×8 1÷0.125 0.25×0.4 0.8×1.25 1.4×0.5 5×0.2 0.06×1.5 6.用简便方法计算下面各题. (1)5.5×17.3+6.7×5.5 (2)13.7×0.25×8 (3)32.8+5.6+7.2 (4)4.6×2.5×40 (5)12.5×3×3×8 (6)50×0.47×0.2 (7)101×7.3 (8)10.1×54 (9)42.6-2.77-7.23 (10)16.4-16.4×0.5 (11)2.18+4.65+7.82+4.35 (12)12.48-2.72-3.28 (13)(250+2.5)×4 (14)4×7×0.5×3×5 (15)(125+1.25)×8 (16)775+10.9+9.1+225 (17)12.4-2.68-7.32 (18)7×1.785+3×1.785 (19)5.25÷15+3.75÷15 (20)18.4×1.7+18.4×8.3 (21)7.6×5.3+7.6×3.7+7.6 (22)45.6÷38-7.6÷38 (23)(0.45+0.06+1.5)÷0.15 (24)2.75÷54+2.65÷54 (25)1.25×8.8 (26)0.89×10.1 (27)25×5.26×40 (28)0.125×32×25 (29)0.36×0.5+0.36×0.4+0.36×0.1 (30)0.38+13.4+1.62+4.6 (31)0.125×78×80 (32)9.1×1.1-9.1×0.1 (33)0.125×32×25×58 ※(34)1.86×1.3+1.86×5.7+1.86×2+1.86 (35)79×0.99+21.79