Page 49 - 振昆讲速算

40. 一个数为625倍数的乘法

625倍数的数如1875,3125,4375,5625,6875,8125等，设另一数为A，则

1
1
1
3
A×1875=A× 30000 =A×10000× =A×10000× 4−1 =A×10000× ( - 1 )=A×10000× ( 1 - )
16 16 16 4 16 4 4
50000 5 4+1 1 1 1 1
A×3125=A× =A×10000× =A×10000× =A×10000× ( + )=A×10000× ( 1 + )
16 16 16 4 16 4 4
70000 7 8−1 1 1 1 1
A×4375=A× =A×10000× =A×10000× =A×10000×( - )=A×10000× ( 1 - )
16 16 16 2 16 2 8

90000 9 8+1 1 1 1 1
A×5625=A× =A×10000× =A×10000× =A×10000×( + )=A×10000× ( 1 + )
16 16 16 2 16 2 8

例1. 3 9 5 4 7×3 1 2 5 =3 9 5 4 7 0 0 0 0× ( 1 + ) =
1
1
4 4
1
3 9 5 4 7 0 0 0 0× = 9 8 8 6 7 5 0 0
4
1
+ 9 8 8 6 7 2 0 0× = + 2 4 7 1 6 8 7 5
4
1 2 3 5 8 4 3 7 5

1
例2. 7 4 3 5 9×4 3 7 5 =7 4 3 5 9 0 0 0 0× ( 1 - )=
1
2 8
7 4 3 5 9 0 0 0 0× = 3 7 1 7 9 5 0 0 0
1
2
- 3 7 1 7 9 5 0 0 0× = - 4 6 4 7 4 3 7 5
1
8
3 2 5 3 2 0 6 2 5

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