Computing power of multi digit numbers

1. 1 / 6 first of all, it is clear that the knowledge system
multiplication of multiple digits by one digit is based on children's learning and mastering multiplication in the table (i.e. multiplication formula) and addition and subtraction within 100. Therefore, mastering these two knowledge points is the premise of learning how to multiply multiple digits by one digit< The first level is oral multiplication. First, learn how to multiply the whole ten, the whole hundred, the whole thousand by one digit and the two digit by one digit
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the second level is to multiply multiple digits by one digit. From carry to carry to multiply with 0 in the middle and at the end of the multiplier. Understand the meaning of each step in the vertical calculation
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the third level is: solving problems (solving practical problems). It is divided into solving problems by estimation and solving problems by multiplication and division
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finally, understand the calculation principle and make clear the practice
multiply multiple digits by one digit: multiply each digit of another multiplier with one digit, and then add the proct
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in addition, mastering how to multiply multiple digits by one digit requires proper practice. Besides, we should connect with life more and improve our ability to solve problems.

2.

The fast calculation method of multi digit multiplication is as follows:

1, more than ten times more than ten: Formula: head by head, tail by tail, tail by tail. Example: 12 × 14= Solution: 1 × 1=12＋4＝62 × 4＝812 × 14 = 168 note: if the number of digits is multiplied by each other, if the number is less than two digits, 0 should be used

2, the head is the same, the tail is complementary (the tail is equal to 10): Formula: after a head plus 1, the head multiplies the head, and the tail multiplies the tail. Example: 23 × 27= Solution: 2 + 1 = 32 × 3＝63 × 7＝2123 × 27 = 621 note: if the number of digits is multiplied by each other, if the number is less than two digits, 0 will be used

3. The first multiplier complements each other, and the other multiplier has the same number: Formula: after one head plus one, the head multiplies the head, and the tail multiplies the tail. Example: 37 × 44= Solution: 3 + 1 = 44 × 4=167 × 4=2837 × 44 = 1628 note: if the number of digits is multiplied by each other, if it is less than two digits, 0 will be used

The pithy formula is: head by head, head plus head, tail by tail. Example: 21 × 41= Solution: 2 × 4=82+4=61 × 1=121 × 41 = 861

5, 11 times any number: pithy formula: head and tail do not move down, the sum of the middle pull down. Example: 11 × 23125= Solution: 2 + 3 = 53 + 1 = 41 + 2 = 32 + 5 = 72 and 5 are at the beginning and end of 11, respectively × 23125 = 254375 note: with the full ten to enter one

< H2 > extended data

multiplication principle:

if the dependent variable f is directly proportional to the independent variables x1, X2, X3,.... xn, and each independent variable is qualitatively different, without any independent variable, the dependent variable f will lose its meaning, it is multiplication

in probability theory, there are n steps for an event to proce results. The first step includes M1 different results, the second step includes M2 different results,..., and the nth step includes Mn different results. Then this event may appear n = M1 × M2 × M3 ×……× Mn is a different result

let a be m × The matrix of n

It can be proved that AX = 0 and a & # 39; The same solution of two homogeneous equations with n-variables AX = 0 proves that R (A & # 39; A) Ax = 0 is definitely a & # 39; Ax = 0, easy to understand

2、A' Ax=0 → x' A' Ax=0 → (Ax)' Ax = 0 → AX = 0

so the two equations have the same solution

In the same way, R (AA & # 39;) can be obtained= r(A')

In addition, R (a) = R (A & # 39;)

In conclusion, R (a) = R (A & # 39;)= r(AA')= r(A' A)

3.

The fast calculation method of multi digit multiplication is as follows:

1, more than ten times more than ten: Formula: head by head, tail by tail, tail by tail
example: 12 × 14=
solution: 1 × 1=1
2＋4＝6
2 × 4＝8
12 × 14 = 168
note: if the number of indivial digits is multiplied by each other, if it is less than two digits, 0 should be used

2. The head is the same and the tail is complementary (the sum of the tails is equal to 10): Formula: after a head plus 1, the head multiplies the head and the tail multiplies the tail
example: 23 × 27=
solution: 2 + 1 = 3
2 × 3＝6
3 × 7＝21
23 × 27 = 621
note: if the number of digits is multiplied by one, if it is less than two digits, 0 should be used

3. The first multiplier complements each other, and the other multiplier has the same number: the formula: after a head plus 1, the head multiplies the head, and the tail multiplies the tail
example: 37 × 44=
solution: 3 + 1 = 4
4 × 4=16
7 × 4=28
37 × 44 = 1628
note: if the number of digits is multiplied by one, if it is less than two digits, 0 should be used

The pithy formula is: head by head, head plus head, tail by tail
example: 21 × 41=
solution: 2 × 4=8
2+4=6
1 × 1=1
21 × 41 = 861

5, 11 times any number: pithy formula: head and tail do not move down, the sum of the middle pull down
example: 11 × 23125=
solution: 2 + 3 = 5
3 + 1 = 4
1 + 2 = 3
2 + 5 = 7
2 and 5 are at the head and tail
11, respectively × 23125 = 254375
note: when he is ten, he must enter one

The pithy formula: the first digit of the second multiplier doesn't fall, the first digit of the first factor is multiplied by each digit after the second factor, the next digit is added, and then it falls
example: 13 × 326=< The 13 bits are 3
3 × 3+2=11
3 × 2+6=12
3 × 6=18
13 × 326 = 4238
note: one must be added to the sum of ten

4. For example, 79 * 13 = 80 * 13-13
for another example, 63 * 25 = 63 * 4 * 25 / 4
3, more vertical operation, practice makes perfect
4, there is a strange line multiplication, such as 12 * 15
vertical drawing |||||||||||||||
let them intersect
oblique view, there are three rows of intersection points, the first row is ||||||||||||||||, The second row is the intersection of |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

5. Let's start with the high order of division, such as 3276 ÷ 24, the divisor is 24, which is a two digit number. Then, we can see that the highest two digits of the divisor are 32, which can be up to 1, and there are 8 and 8 left in the hundreds. We can also find the 7 of the ten digits, that is, 87 divided by 24, which can be up to 3, and the remaining 15, which can be down to the low level if it is not enough.
generally speaking, it is not difficult to divide the multi digit number into several two digit numbers, starting from the high level, The remainder is the highest of the next two digits. If the divisor is a 3-digit number, it can be divided into several 3-digit numbers, and so on.

6. Add: first add from one digit, every decimal one, in to ten, hundred, and so on to get the final result
subtraction: start with the subtraction of indivial digits, and if it is not enough to borrow from ten digits, one will be subtracted, and ten digits will be subtracted by one; From the first to the tenth, and so on

7. The number is represented by fingers
based on fingers. Memorizing ten digits in the brain and showing single digits by hand can rece the burden of thinking and calculation, and it is also concive to the ability of oral calculation. Most people write with their right hand and count with their left hand
the fingers with the same direction as the thumb are called the outer fingers of the number, and the fingers with the opposite direction are called the inner fingers of the number
1. Thumb flexion indicates 1. In this case, the external reference of 1 is 1 and the internal reference is 4
2. Flexion of thumb and index finger at the same time indicates 2. In this case, the outside finger of 2 is 2 and the inside finger is 3

5. In this case, the external reference of 5 is 5 and the internal reference is 0
6. Thumb extension indicates 6. In this case, the outer finger of 6 is 1 and the inner finger is 4

10. Full extension of five fingers means 0. In this case, the outer reference of 0 is 5 and the inner reference is 0
make up: the sum of the two numbers is equal to 5, and they make up for each other. For example: 1 and 4
mantissa: the mantissa of a number greater than 5 but less than 10 minus 5. For example, the mantissa of 6 is 1
complement: the sum of the two numbers is 101001000... They complement each other. For example: 4 and 6

8. From the top to the bottom, the quotient will be written on the top.

9. Multi digit number refers to the number composed of three or more digits, which is called multi digit number.

10. There are two kinds of division: division by return and division by quotient.
division is calculated by pithy formula, including nine return pithy formula, withdrawal pithy formula and nine quotient pithy formula.
nine return pithy formula has 61 sentences:
one return (divided by 1): every one enters one, every two enters two, every three enters three, every four enters four, every five enters five, every six enters six, every seven enters seven, every eight enters eight, Every nine into nine.
two returns (divide by 2): every two into one, every four into two, every six into three, every eight into four, 21 into five.
three returns (divide by 3): every three into one, every six into two, every nine into three, 31 into three, 32 into three, 32 into two.
four returns (divide by 4): every four into one, every eight into two, 42 into five, 41 into two, Four three seven more than two.
five GUI (divide by five): every five into one, five one times make two, five two times make four, five three times make six, five four times make eight.
six GUI (divide by six): every six into one, every twelve into two, six three add five, six one add four, six two three more than two, six four six more than four, six five eight more than two.
seven GUI (divide by seven): every seven into one, every fourteen into two, Seven one adds three, seven two adds six, seven three four more than two, seven four five more than five, seven five seven more than one, seven six eight more than four.
eight GUI (divide by eight): every eight enters one, eight four adds five, eight one adds two, eight two adds four, eight three adds six, eight five six more than two, eight six seven more than four, eight seven seven more than four, eight seven eight more than six.
nine GUI (divide by nine): every nine enters one, nine one adds one, There are nine sentences in the formula of quitting business:
one without quitting business, two without quitting business, three without quitting business,
four without quitting business, five without quitting business, five without quitting business, six without quitting business,
seven without quitting business, The formula of Shang Jiu consists of nine sentences:
see one nothing except for ninety-one, see two nothing except for ninety-two, see three nothing except for ninety-three,
see four nothing except for ninety-four, see five nothing except for ninety-five, see six nothing except for ninety-six,
see seven nothing except for ninety-seven, see eight nothing except for ninety-eight, see nine nothing except for ninety-nine