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 =/.