Computing power of two digit multiplication

1.

Multiply with a cross

that is to calculate the multiplication result of one digit, then multiply the result of ten digits, and then multiply the result of one digit and ten digits respectively. After adding, if more than one digit, it will be added to the multiplication result of ten digits. If one digit is ten, it will be the same for one digit

for example: 54 * 32 can be calculated in this way: bit: 2 * 4 = 8; Ten: 5 * 3 = 15; Finally, 5 * 2 = 10; 4 * 3 = 12, 10 + 12 = 22, the final result is: 1728

2. (1) Head with tail ten:
63 × 67 = 4221 (the first two digits are 6 × 6+1=6 × 7 = 42, the last two are 3 × 7.=21
51 × 59 = 3009 (front 5) × 6 = 30, the last two are 1 × 9=09
78 × 72 = 5616 × 78 = 2964 (first two digits 3) × 7 + 8 = 29, the last two digits are 8 × 8=64
79 × 39 = 3081 (front two digits 3) × 7 + 9 = 30, the last two are 9 × 9=81

3. Unknown_Error

4.

The fast calculation method of two digit multiplication is shown in the following table:

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the partial inference method of two digit multiplication:

let two digits be 10A + B, 10C + D respectively, and the proct be s. according to the polynomial expansion:

s = (10a + b) x (10c + D) = 10A x 10C + B x 10C + 10A x D + BXD

First, the first number is the same, and the last number is complementary (the sum of two numbers equals 10 is called complementary)

because the single digits are complementary, B + C = 10

(10a + b) (10a + C)

= 100A & amp# 178;+ 10a(b+c) +bc

= 100a&# 178;+ 10A X10 + BC

= 100A (a + 1) + BC

quick calculation method:

1

Then connect the proct of two mantissa

example:

25x25 = | (2 + 1) x 2 | 5 x 5 | = | 6 | 25 | = 625

36X34 = | (3 + 1) x 3 | 6 x
4 | = | 12 | 24 | = 1224

2. The first number is the same, and the last number is not complementary

(10a + b) (10a + C)

100A & amp# 178;+ 10A (B + C) + BC

= 10A (10a + B + C) + BC

= ((10a + b) + C) x 10A + BC

quick calculation method 1:

< P > 1

Then multiply the second multiplier by the remaining number

Finally, add the proct of two mantissa

example:

72 * 73 = (72 + 3) x 70 + 2 * 3 = 5256

quick calculation method 2:

1. Calculate the square of the first digit, and the resulting number is the proct

When the sum of two mantissa is multiplied by the first one, the resulting number is regarded as the middle proct

When two mantissa are multiplied, the resulting number is regarded as the post proct

application example:

64 x 67

6 x 6 = 36

(4 + 7) x 6 = 66

4 x 7 = 28

the result is: 4288 (36 + 6 = 42; 28 + 60 = 88)

three, the first number is complementary, the last number is the same

ten digit complementary, so there is a + C = 10

(10a + b) (10c + b) = 100ac + 10 (Ba + BC) + B & amp# 178;= 100ac + 10b(a + c) + b&# 178;

=100ac + 10bx10 + b&# 178;

=100(ac + b) + b&# 178;

Fast calculation method:

1

The multiplication of two mantissa, that is, the square of mantissa, results in the number as the post proct, and there is no ten place complement 0

Application examples:

< P >

> + B & amp# 178;= 100ac + 10b(a + c) + b&# 178;

Fast calculation method:

1

The sum of the two first numbers is larger or less than 10

The mantissa will be added to the number of

larger than 10

The number of

less than 10 will be reced by several mantissa

The position of

addition and subtraction is: one digit ten digit addition and subtraction; Two digit hundred addition and subtraction

results were regarded as the median proct

The mantissa are multiplied by each other as the post proct

application example:

67 x 87 = | 6 x 8 + 7 | 7 x 7 | + (6 + 8 - 10) x 7 x 10 = 5549 + 280

= 5829

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7. In general, the distribution law of multiplication is used to calculate skillfully, such as 9 × 124=10-1 × 124=1240-124=1116

8. If the multiplication of any two digits (including more digits, such as three digits, etc.) is calculated in writing, the vertical multiplication is used
24
× 35
-
120 do 24 first × 5 = 120, align the last bit of the result with the indivial bit
72, and then do 24 × 3 = 72, the last bit of the result is aligned with the ten bits (which bit of the multiplier and the multiplicator are multiplied, the result is aligned with that bit)
-
840 add the two results according to the aligned bits (if there is carry, it is the same as the ordinary addition), and the result is the proct
24 × 35=840

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