Abacus mental arithmetic multiplication formula

Division formula: There are two kinds of abacus division: subtraction division and quotient division.

Division is calculated by formulas, including nine formulas, regression formula and quotient formula.

Alcoholic formula ***6 1 sentence:

One time (divided by 1): one time, two times, three times, four times, five times, six times, seven times, eight times and nine times.

Two returns (divided by two): every two into one, every four into two, every six into three, every eight into four, 2 1 plus five.

Three returns (divided by three): three into one, six into two, nine into three, three into one, three into two.

Four returns (divided by four): every four enters one, every eight enters two, four two adds five, four twelve is more than two, and four thirty-seven is more than two.

Five cycles (divided by five): every five cycles into one, 5 1 cycle is two, 52 cycles is four, 53 cycles is six, and 54 cycles is eight.

Six returns (divided by six): one every six, two every twelve, six three plus five, six one plus four, six two three left two, six four left four, six five eight left two.

Seven returns (divided by seven): every seven returns to one, every fourteen to two, every seven to three, every seven to six, every seven to four, every seven to five, every seven to five and every seven to four.

Eight returns (divided by eight): every eight enters one, 84 adds five, 8 1 adds two, 82 adds four, 83 adds six, 856 is greater than two, 867 is greater than four, and 878 is greater than six.

Nine returns (divided by nine): every nine returns to one, nine returns to one, ninety-two returns to two, ninety-three returns to three, ninety-four returns to four, ninety-five returns to five, ninety-six returns to six, ninety-seven returns to seven and ninety-eight returns to eight.

Back to business formula ***9 sentences:

Only refund, only refund, two, three,

Did not return 4, did not return 5, did not return 6,

No return 7, no return 8, no return 9,

Nine business formulas ***9 sentences:

See no score 9 1, see no score 92, see no score 93,

See four division is 94, see five division is 95, and see six division is 96.

Don't divide 97 by seven, 98 by eight, and 99 by nine.

Division with a divisor of single digits is called "single return"; Division with two or more divisors is called division, the first divisor is called division, and the following digits are called division. For example, if the divisor is 534, it is called "five divided by three divided by four". That is, the formula of dividing the quotient by 34 after using the formula of 5? The simple operation of finding the sum of several identical addends is called multiplication. Or find a number several times the calculation method is called multiplication. Abacus multiplication can be divided into pre-multiplication and post-multiplication in the order of multiplication. The multiplication before the empty disk is fast, the grade is clear and the accuracy is high, which is suitable for children to learn. Therefore, this book focuses on the multiplication before the empty disk. 1. The traditional abacus multiplication in China uses multiplication formula. As long as you master and memorize the formula of 99, you can calculate the product quickly and accurately. The 999 formula includes 9945 sentences, 36 sentences of inverse 999, and * * 8 1 sentence. There are tables in the book, which are omitted here. ) In abacus calculation, we put \ \ \ in order to make it easier to dial the beads. Such as: 1202, 2204, 34 12. The first two digits of each formula represent multiplicand and multiplier, and the last two digits represent product. According to one multiplication formula, two multiplication formulas can be written. For example, 4624 can be written as: 4×6=246×4=24.

2. Product positioning method. Abacus multiplication requires accurate product, so we must master the positioning method of product. There are many positioning methods for abacus products. This paper mainly introduces the commonly used formula positioning method and fixed file positioning method. The positioning of digital product of (1) number is based on the number of multiplicand and multiplier. Therefore, to learn the multiplication positioning method, we must master the number of digits. There are three kinds of digits in a number: ① positive number. A number has several integers, which are called positive (+) digits. [Example]: 1 is positive (+) 1 digit. 32 is a plus (+)2 digit. 128.03 is a positive (+)3 digit, which is called a negative (-) digit. [Example]: 0.025 is negative (-) 1 digit. 0.003 1 is negative (-)2 digits. 0.000 16 is a negative (-)3 digit. 0.00007 1 is negative (.

(2) Formula positioning method Formula positioning method is also called general positioning method. We use m to represent the number of digits of the multiplicand and n to represent the number of digits of the multiplier. Adding the sum of the digits of the multiplicand, comparing the first digit of the product with the first digit of the multiplicand and the first digit of the multiplier, and determining the product with a certain formula is called formula positioning method. There are two ways to locate the multiplication formula: ① The first bit of the product is less than the first bit of the multiplicand and the first bit of the multiplier. Number of digits of product = m+n ② The first digit of product is greater than multiplicand and multiplier, and the number of digits of product =m+n- 1. [Example]: 46×24= 1, 104 The first digit of the multiplicand is 4, the first digit of the multiplier is 2, and the first digit of the product is 1 604. 4 1 & lt； 2. Use the formula m+n to locate: (+2)+(+2)=+4 (bit). The product is 1, 104. [Example]: 2 1.6×3. 1=66.96 The first multiplicand is 2, the multiplier. 2,6 > 3. use the formula m+n- 1 to locate: (+2)+(+ 1)- 1=+2 (bit). Product 66.96. If the first bit of the product is the same as the first bit of the multiplicand and the first bit of the multiplier, it is superior to the second and third bits. Compared with the second place, the multiplicand, multiplier and product are all 0; The same is true of the third digit. Use the formula m+n- 1 to locate: (+3)+(+3)- 1=+5 digits, and the product is 10000.

(3) Fixed file positioning The legal file positioning method is pre-calculated positioning. This method is simple and convenient. Before operation, set a file. Use m to represent the multiplicand digits, use n to represent the multiplier digits, and use the multiplicand digits to add the multiplier digits, that is, use m+n to determine the highest level of the product. There are three situations. When m+n is equal to a positive number, the highest grade of the product is in a positive number; When m+n is equal to negative number, the highest level of product is negative number; When m+n is equal to zero, the highest grade of the product is zero. After the operation, the number on the plate is the product. [Example]: 723× 35 = 25,305,637.2×150.7 = 96,026.04.

3. Multiplication before the empty disk multiplication operation In the multiplication operation, two numbers are multiplied, and the multiplicand is multiplied by the multiplier. From the first bit to the last bit of the multiplier, the product is calculated in this operation order. Because the multiplier and multiplicand are not put on the disk, it is called multiplication before empty disk. Its advantages are high speed, high accuracy and easy learning. Blank multiplication is used in abacus multiplication and abacus mental multiplication in this book. (1) Intra-table multiplication is the multiplication within the range of multiplication formula, that is, the multiplication of two digits, which is the basis of multi-digit multiplication, so we should firmly grasp it. [Example]: 6× 2 = 12 4× 2 = 88× 5 = One of the multiplier and the multiplicand is a one-digit multiplication. The operation steps are as follows: Step 1: Locate the highest grade of the product. That is to say, the highest level of the product is determined by the method of fixed one-bit file position, and the multiplier is seen by the formula m+n, and the multiplicand is memorized. Step 2: Multiply the multiplicand bit by bit with the multiplier, starting from the first bit of the multiplicand and then reaching the last bit. Step three. Ten digits of the product are added to the highest place of the product, and single digits are added to the right file. When the multiplier is multiplied by the second and third bits of the multiplicand until the last bit, each product is added out of place. Step 4: The operation is terminated, and the number of disks is the product.

The multiplicand is a two-digit number and the multiplier is a one-digit number. [Example] 32×3=96 24×4=96 76×3=228 The multiplicand is a three-digit multiplication. [Example]: 814× 3 = 2,442,437× 6 = 2,622 5. Multiplier is the multiplication of one digit. [Example]: 4,378× 6 = 26,268 45,067× 4 =180,268 8.764× 4 = 35.06 (exactly 0.0 1).

(3) Multi-digit multiplication Multi-digit multiplication is the multiplication of two numbers. When both the multiplier and the multiplicand are more than two digits, it is called multi-digit multiplication. The operation method of multi-digit multiplication is basically the same as that of single-digit multiplication. Multiplier and multiplicand are easy to add the wrong file. Therefore, just like one-digit multiplication, we must master the gear of addition product. First, multiply each bit of the multiplicand with the first bit of the multiplier in turn; Multiply the digits of the multiplicand by the second digit of the multiplier in turn ..... until the digits of the multiplicand are multiplied by the last digit of the multiplier in turn, and the product is added by dislocation. Multiplier is the product of two digits [example]: 32× 12=384 764×56=42 784 3.14× 4.7 =14.76 (accurate to 0.0 1) Multiplier is three digits or three digits. [Example]: 347× 628 = 217,9163,476× 8.

Note: The steps are as follows: 1. Positioning and products are the highest grade; 2. The order sum product of multiplication.