1, both factors are within 20.
The product of any two digits within 20 can shift the mantissa of one factor to another factor, and then add a 0 to add up the products of the two mantissas. For example:
1 1× 1 1= 120+ 1× 1= 12 1
12× 13= 150+2×3= 156
13× 13= 160+3×3= 169
14× 16=200+4×6=224
16× 18=240+6×8=288
2. These two factors are between 10 to 20 and 20 to 30 respectively.
For the product of either of these two factors, the mantissa of the smaller factor can be shifted twice to the other factor, then a zero is added, and then the product of the two mantissas is added. For example:
22× 14=300+2×4=308
23× 13=290+3×3=299
26× 17=400+6×7=442
28× 14=360+8×4=392
29× 13=350+9×3=377
These two factors are both between 20 and 30.
For the product of any of these two factors, you can add the mantissa of one factor to the other factor to get the product, and then add the products of the two mantissas. For example:
22×2 1=23×20+2× 1=462
24×22=26×20+4×2=528
23×23=26×20+3×3=529
2 1×28=29×20+ 1×8=588
29×23=32×20+9×3=667
After mastering this method, the product of two factors within 30 can be quickly calculated in mind.
Second, mental arithmetic of the product of two digits greater than 70.
For the product of any of these two factors, one of them can be used to make up the other factor into the product of 100, plus the product of 100 and the difference of these two factors respectively. For example:
99×99=98× 100+ 1× 1=980 1
97×98=95× 100+3×2=9506
93×94=87× 100+7×6=8742
88×93=8 1× 100+ 12×7=8 184
84×89=73× 100+ 16× 1 1=7476
78×79=57× 100+22×2 1=6 162
75×75=50× 100+25×25=5625
After mastering the above two methods, the product of two factors within 30 and the product of two digits greater than 70 can be quickly calculated in mind.
Three, more than 50 and less than 70, the mental arithmetic of the product of two digits.
For the product of either of these two factors, the smaller factor greater than 50 can be added to the product of the other factor, and then the difference between the two factors can be added to the product of 50. (Multiplying a factor by 50 is equal to dividing the factor equally and then multiplying it by 100) For example:
5 1×5 1=26× 100+ 1× 1=260 1
53×59=3 1× 100+3×9=3 127
54×62=33× 100+4× 12=3348
56×66=36× 100+6× 16=3696
66×66=4 1× 100+ 16× 16=4356
Four, more than 30 and less than 50, the mental arithmetic of the product of two digits.
For the product of either of these two factors, you can use the smaller factor to make the other factor a product of 50, and then add 50 to the product of the difference between these two factors. (Multiplying a factor by 50 is equal to dividing the factor equally and then multiplying it by 100) For example:
49×49=24× 100+ 1× 1=240 1
46×48=22× 100+4×2=2208
44×42= 18× 100+6×8= 1848
37×47= 17× 100+ 13×3= 1739
32×46= 14× 100+ 18×4= 1472
Fifth, the multiplication speed algorithm
Multiplication speed algorithm is a simple and easy-to-master multiplication speed algorithm, which changes the traditional algorithm into complement method. For example, 49×47 can be changed to 50×46+ 1×3=2303 and 98×94 can be changed to 100× 92+2× 6 = 9265438. Tail shift method, for example: 5 1×53 can be changed to 50×54+ 1×3=2703, and 3 1×32 can be changed to 30× 33+/kloc-0 /× 2 = 992; Supplementary commercial laws, such as: 84×24 can be changed to 100×20+4×4=20 16, etc. One by one, note that a factor multiplied by 50 equals this factor multiplied by 100.
1, complement method
For the product of any two factors, you can use one of them to make up the other factor into an "integer" to find the product, and then add this "integer" to the product of the difference between these two factors. For example:
19× 19= 18×20+ 1× 1=36 1
27×28=25×30+3×2=756
46×48=44×50+4×2=2208
94×99=93× 100+6× 1=9306
87×98=85× 100+ 13×2=8526
38×48=36×50+ 12×2= 1824
Complement method is more suitable for multiplication with the sum of the beginning and the end not less than 10, especially for multiplication with two factors slightly less than 20, 30, 50 and 100.
2. Tail shift method
For the product of any two factors, you can add the mantissa of one factor to another factor to get the product, and then add the difference between the two factors to the product of this integer. For example:
14× 12= 16× 10+4×2= 168
22×23=25×20+2×3=506
55×5 1=56×50+5× 1=2805
62×54=66×50+ 12×4=3348
43×37=50×30+ 13×7= 159 1
1 12× 103= 1 15× 100+ 12×3= 1 1536
The tail-shifting method is more suitable for the multiplication in which the sum of the first approximation to the tail is not greater than 10, especially for the multiplication in which both factors are slightly greater than 10, 20, 30, 50 and 100.
3. Supplementary commercial law
Let a, b, c and d be undetermined numbers, then the product of any two factors can be expressed as:
AB×CD=(AB+A×D/C)×C0+B×D
The complementary business method is especially suitable for multiplication in which c is divisible by a× d. For example:
23× 13=29× 10+3×3=299
33× 12=39× 10+3×2=396
46× 1 1=50× 10+6× 1=506
28×77=30×70+8×7=2 156
82×55=90×50+2×5=45 10
8 1×24=97×20+ 1×4= 1944
76×36=90×30+6×6=2736
When c is not divisible by A×D, AB can add the integer parts of A×D/C, and the remainder will add dozens to the original result. For example:
84×65=90×60+40+4×5=5460
73×32=77×30+20+3×2=2336
After mastering this method, the product of two factors within 130 can basically be calculated quickly in mind.
Six, the product of two numbers close to 100 mental arithmetic skills
For calculating the product of any two-digit number greater than 90 and the product of any two-digit number less than 1 10, you can do mental arithmetic accurately, quickly and clearly through clever speed calculation methods.
1, the product of two three digits is less than 0 of 1 1.
For the product of any two three-digit numbers less than 1 1 0, the product must be five digits, the three digits on the left are always equal to the mantissa of one factor plus another, and the two digits on the right are always equal to the product of two mantissas. For example:
108× 109= 1 1772。 The three digits on the left are equal to 108+9= 1 17, and the two digits on the right are equal to 8×9=72. Similarly:
105× 107= 1 1342
104× 109= 1 1336
102×103 =10506, and the two digits on the right are 2×3=6, so it should be written as 06. Similarly:
10 1× 109= 1 1009
103× 103= 10609
2. The product of any two digits greater than 90.
For the product of any two-digit number greater than 90, the product must be four digits. The two digits on the left are always equal to 80 plus the mantissa of two factors, and the two digits on the right are always equal to the product of 100 and the difference between these two factors. For example:
9 1×92=8372, two digits on the left are equal to 80+ 1+2=83, and two digits on the right are equal to (100-91) × (100-92) = 72. Similarly:
93×93=8649
94×94=8836
95×96=9 120
99×98=9702, and the two digits on the right are equal to 1×2=2, so it should be written as 02. Similarly:
99×99=980 1
97×97=9409
Multi-digit multiplication:
9997*9478
Move 9478 three places to 9997, and you get 9475 * 10000 = 94750007, 9997 and 3' s complement get 10000, and the difference between 9478 and 522 get1000005, 3 * 522 =/.