无限系统之斗破苍穹.:五年级奥数专题解析；小数四则混合运算简算_小学题库_好父母教育咨询网_www.haofum...

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