Quickly calculate the secret in one minute! (One-minute quick calculation can definitely be tried)
Seeing the “one-minute quick calculation formula” mentioned on TV as an example, I think it is very good, so I want to share it with you: multiply two digits, ten The number of digits is the same, when the single digits add up to 10, such as 6268=4216. Calculation method: 6(6+1)=42 (front product), 28=16 (back product). The theorem of the one-minute quick calculation formula for special problems is: as long as any two-digit number is multiplied by any two-digit number, the product obtained by the Wei coefficient is “0”, and it must be the product obtained by multiplying the tails of two binomials by the tails. The product, the product obtained by multiplying the head by the head (the sum of one item plus one) is the front product, and the product obtained by two adjacent products.
For example, (1) 3346=1518 (the sum of single digits is less than 10, so the number 3 of the small tens digit remains unchanged, and the number 4 of the large tens digit must plus 1). Calculation method: 3(4+1)=15 (front product), 36=18 (back product). Two products form 1518, such as (2) 8443 = 368. 34 = 12 (post product) The composition of two adjacent products: 3612 as shown in (3) 4826 = 1248 Calculation method: 4 (2 + 1) = 12 (pre-product), 68=48 (rear product) the composition of two products: 1248 as shown in (4) 245 square=60025abcd Calculation method 24 1. Find the Wei type coefficient first. 2. One of the products (one plus one) is the front product (the tail adds up to 10). 3. The tail product is the back product. 4. When the two products are connected, the Wei-type coefficient can be added to ten digits. For example, 7675, 8784, the sum of the single digits of the same tens digit is 11, then its Wei-type coefficient must be its tens digit.
For example, the coefficient of the 7675 Guardian is 7, and the coefficient of the 8784 Guardian is 8. For example, 7863, 5942, their coefficients must be the tens digit minus its one digit. For example, the Wei-type coefficient of the first question is equal to 7-8=-1, and the Wei-type coefficient of the second question is equal to 5-9=-4. As long as there is one difference between the tens digits, then the ones digits add up to 11, which can be quickly calculated by the above method. Example 1 7675, calculation method: (7+1)7=56 56=30 Two products form 5630, then add 7 to the tens digit, the final product is 5700. Example 2 7863, calculation method: 7(6+1)=49, 38=24, the two products add up to 4924, then subtract 1 from 2 in the tens digit, and the final product is 4914. (1) One dozen times one dozen, this is the easiest way. Reserve the tens digit plus one, plus zero plus one. It is proved that if m and n are any integers from 1 to 9, (10+m)(10+n)= 100+10m+10n+Mn = 10[10+(m+n)]+Mn. Example: 17l 6: 10+(7+6)= 23 (third sentence), ∴ 230+76 = 230+42 = 272 (fourth sentence), ∴1716 = 272.
(2) Multiply the tens digits with the same and complementary two digits (the sum is 10) by the tens digits, each digit will be complementary. Remember: the tens digit plus one times the tens digit is followed by the product of each digit. Proof: Suppose m and n are any integers from 1 to 9, then (10m+n)[10m+(10-n)]=100m(m+1)+n(10-n). Example: 3436: (3+1)3 = 43 = 12 (third sentence), the product of units is 46 = 24, ∴ 3436 = 1224. (Fourth sentence) Note: When the product of two numbers is less than 10, the tens digit should be written as zero. (3) Multiply any other two-digit number by 11. Both sides of this number go to Youyou Resource Network, leave a space in the middle, and add it with sum. Proof: Let m and n be arbitrary integers from 1 to 9, then (10m+n) (10+1) = 100m+10 (m+n)+n. Example: 3611: 306+90=396, ∴ 3611= 396. Note: When the sum of the two digits is greater than 10, if the hundreds digit is required, then the hundreds digit becomes M+1, for example: 8411: 804+1210 = 804+120 = 924, ∴ 8411 = 924. Two-digit multiplication quick calculation formula General formula:
One of the products is ranked first, and the sum of the first and the last cross product is ten times plus the last product. For example, 37×64=1828+(3×4+7×6)x10=23681, the same tail is complementary, one of which is multiplied by the larger one, and then the product of the tail. For example: 2327=6212, the tail and the head are complementary, the product of the head adds the tail, and the product of the tail follows. 827 = 23493. If one of the differences is a mantissa’s complement, reduce one of the large numbers and the last square. For example, 7664=48644, the last digit is the same, the product of one digit is followed by the sum of one digit, and the product of the last digit is followed by the last digit. For example: 5121 = 1071——”Several elevens multiplied by several elevens” is special: it is used for the square of one, such as 2121=4415, the beginning and the end are different, one number is added to the other end, and the product of the end is added After a multiple of the whole one. 325 = 575 quick calculation 1), one of the digits is one, one number plus the tail of another number, ten times the product of the tail. 719 = 323 – the quick calculation of “a dozen multiplied by a dozen” includes the square of the tens digit is 1 (ie 11~19), such as 1111 = 121 – the quick calculation of “a dozen square” 2) one of the digits is Yes, the other digits plus one digit, the product of the twenty digits times the mantissa. 529 = 725-“20 times 20″ quick calculation 3) One of the digits is five, the mantissa product is behind the 25th digit, and the sum of the hundreds digit plus the mantissa is half. 557 = 3249——”Fifty times fifty” quick calculation 4) One of the digits is nine, eighty plus two mantissas, followed by the product of mantissa complements. 999 = 9405——”Ninety plus ninety” quick calculation 5) One digit is the square of four squares, fifteen plus the tail, and the square behind the tail is a square. 446 = 2116—”40 square meters” quick calculation 6) One digit is five square meters, 25 plus the tail, and the back is the square of the tail. 551 = 2601-“more than 50 square meters”6. If the complement is multiplied by overlapping numbers, one is multiplied by the first of the overlapping numbers, followed by the product of the mantissa. 399 = 3663 7. The last digit is five squares, one digit multiplied by one, and the product of the mantissa. For example, 6565 = 4225 – “ten or fifteen square meters”8. Multiply a certain number by 1, pull it apart from the beginning to the end, and the end is the middle station. For example, 3411 = 3 ^ 3 + 4 ^ 4 = 374 ^ 9. When a number is multiplied by 15, the original number plus half of the original number will be followed by a 0 (the original number is an even number) or the decimal point will be shifted by one. For example, 15115=2265, 24615=369010, one hundred times one hundred, one number plus the tail of another number, the product of the tail follows. For example, 108107=1155611, if the difference between the two numbers is 2, then subtract one from the square of the average of the two numbers. For example, 49×51=50×50-1=249912, multiply the number of numbers by 9, and then use this number to subtract the difference (the number of the first few numbers + 1) to form the first few numbers of the product, the last number and Single digits form several zeros. 1) A number is multiplied by 9: the difference of this number minus (the number of the first few digits + 1) is one of the digits of the product, and the last digit is complemented by 10^49 = 36. Think about it: one bit is 0, 4-(0+1) = 3, and the last bit is 10-4 = 6. The total is 36 7839 = 7047. Think of the previous 78 years. The last digit is 10-3 = 7, which adds up to 70472) Multiply a number by 99: subtract this number (first ten digits + 1), and round the last two digits to 100: 1499 = 14-(0+ 1) = 13, 100-14 = 86 1386 15899 = 158-(1)00-58 = 42 15642 735799 = 7357-(73+1)=.
1. “Nine times nine, left minus right complement, then add two squares, one complement and one complement to write.” The multiplier minus the multiplier’s complement, and then two The product of the complements of a number. If the complement of 9395 95 is 5, 93-5=88, the complement of 93 is 7, 75=35, 9395=8835 principle: 9395 = 93(100-5)= 9300-593 = 9300-5(100- 7) = 930.
2. Multiply any number by 25, divide this number by 4, then divide by 4, make 00, make 25, make 50, make 75. For example, 2425=244=6 complement 00=600, 2525 = 254 = 6-1 complement 25=625.
225 = 264 = 6-2 supplements 50=650, 2725 = 274 = 6-3 supplements 75=675
3. Any number multiplied by 15 is equal to this Count plus half of yourself. Add 5 to odd numbers and 0 to even numbers. For example, 3315=33+16=49 plus 5=495, 3215=32+16=48 plus 0=480.
4. Multiply any number by 55, which is equal to 50% of the number. Complement 5 for odd numbers, 0 for even numbers and multiply by 11. Such as
355 = 372 = 18 complement 5 = 18511 = 2035 3255 = 322 = 16 complement 0 = 16011 = 1760
5.” Ten of the same form 10, ten plus one Multiply by ten, followed by two empty squares, write one by one.” Tens digit: The same ones digit multiplied by two digits is equal to 10, which is equal to the tens digit plus one multiplied by the tens digit, and then the ones digit multiplied by the ones digit. For example, after 3634=(3+1)3=12, write 64=24, 3634=1224.
6. The sum of the two digits of the multiplicand is 10, and the two digits of the multiplier are the same. The algorithm is the same as above. For example, after 3766=(3+1)6=24, write 76=2442 principle: 37 66 = 3060+(760+306)+76 = 3060+(1060)+42 =(30+10)60+42 = 2442 .
Seven. “Ten’s complement is the same, ten times ten plus one, plus two empty squares, one after another”. The tens digit adds up to 10. Multiply two two-digit numbers by the same ones digit, multiply by ten and add one, and write them one by one. For example, after 7838=7 3+8=29, write 88=64, 78 38=2964.
Eight, the multiplication of two-digit numbers with one digit being 1 is equal to ten times ten spaces, then add ten plus ten, and then write 1. For example, 4151 = 45 = 20 _+4+5 = 209 and then write 1=2091.
9. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. Because 343=102, a number that is divisible by 3 multiplied by 34 is divisible by 3 and then multiplied by 102. For example, 13534=45102=45 90, 3934=1326.
73 = 201, you can also use the above technique. For example, 6967=46 23
33 = 111, you can also use the above method. For example, 13537=45111, the two-digit number is multiplied by 111, the beginning and the end are the same, and the middle is added repeatedly. 45111=4(4+5)(4+5)5=4995