abacus requires a formula:

1. Addition formula table: the addition of carry without carry, straight up to five plus ten plus five plus five plus ten. Plus one: one goes up one, one goes down five to four, one goes to nine and enters one. Plus two: two up two, two down five to three, two to eight into one, plus three: three up three, three down five to two, three to seven into one.

2. Add four: four up to four, four down to five to one, four to six into one, plus five: five up to five, five to five into one, six up to six, six up to four into one, six up to five into one, plus seven: seven up to seven, seven up to three into one, seven up to two up to five into one, and eight up to eight, eight up to eight.

3. Subtraction formula table: the reduction of the declining position that does not abdicate, the direct reduction of the declining position that breaks five, and the reduction of ten supplements five. Minus one: one down, one up, four to five, one back, nine, two down, two up, three to five, two back, eight down, three down, three up, two to five, three back, one to seven, four down, four up, one to five, four back, one to six.

4. Subtract five: five times five, five returns one to five, minus six: six times six, six returns one to four, six returns one to five to one, minus seven: seven times seven, seven returns one to three, seven returns one to five to two. Subtract eight: eight down eight, eight back one to two, eight back one to five to three, subtract nine: nine down nine, nine back one to one, nine back one to five to four.

5. Division in which the divisor is a single digit is called "single return"; A division in which the divisor is two or more digits is called "return", the first division is called "return", and the following digits are called "division". For example, the divisor is the division of 534, which is called "five to three and four division". That is, after using the formula of five returns to find the quotient, divide it by 34.

6. The abacus power can be directly multiplied, or according to the formula. If the power of the higher power is a prime number, there is only direct multiplication. If the factor can be decomposed, it can be decomposed and then calculated.

7, abacus square root, generally there are semi-99 square root method, product difference square root method, formula square root method, multiplication square root,? Open cubic, there are three root opening methods and big quotient opening methods. There are many ways to open the fifth power, and the common one is to increase and multiply the fifth power. Generally speaking, it is seldom used in abacus calculation.

Extended data:

1. Abacus formula:

(1) Jiujiu formula:

(2) Addition formula:

(3) Subtraction formula:

(4) Division by abacus:

(5) Division by abacus: < Neutral means that this gear is not counted, or it means .

empty disk: when all gears of the abacus are empty, it means that there is no counting at all, which is called empty disk.

inner bead: the counting beads counted by the beam are called inner beads.

outer beads: counting beads that are not counted from the beam are called outer beads.

pulling up: refers to pulling the lower bead against the beam.

pulling: refers to pulling the upper bead against the beam.

pulling away: refers to pulling the upper bead or the lower bead away from the beam.

this file: it is the file that corrects the number of balls to be dialed.

previous file: it refers to the previous file of this file, also called the left file (bit).

last shift: refers to the last shift of this shift, also called the right shift (bit).

(2) term 2:

floating beads: when pulling the beads, the force is too light, and the beads float in the middle of the file.

with beads: when pulling beads, it is called with beads to bring in or take out the beads that should not be pulled in or out of this file or adjacent files.

solid bead: a bead that represents a positive number by a beam.

virtual bead: also called negative bead, refers to the suspended bead that is set to neither the beam nor the frame, indicating negative numbers.

set number: also called distribution number. According to the requirements of calculation, dial the number into the abacus to prepare for calculation.

gear: also called grade, it refers to the rank of the gear.

wrong gear: also called misplacement, which means that the calculation bead is not put into the proper gear during the operation.

gear shift: also called gear shift, it refers to the second gear (bit) with one gear left and right of this digit. For example, if two numbers are multiplied in interval multiplication, the unit of the product is played on the right two digits of the multiplicand; In every division, every quotient refers to the left two digits of the first dividend.

carry: it means that after adding a number to this file, it is greater than or equal to 1, and 1 must be added to the previous position, which is called carry.

(3) term 3:

abdication: it means that this file is not enough when a number is subtracted from this file, and it is allowed to subtract 1 from the previous one, which is called abdication.

first digit: also called the highest digit, which means that the first non-zero digit of a multi-digit is the first digit. Such as 3 in 3284 and 7 in .726.

Last digit: also called the lowest digit, refers to the last digit of a multi-digit number. Such as ,481.29 out of 5,12 in 3275

.

second digit: the second digit of a multi-digit number. Such as 8 in 3865 and 1 in .4178.

Real number: The multiplicand and dividend are generally called real numbers in ancient arithmetic books.

normal number: multiplier and divisor are commonly called normal numbers in ancient books, which is abbreviated as method.

multiplication and addition: refers to multiplying each bit of the multiplicand by each bit of the multiplier, and adding the product while multiplying on the abacus.

multiplication and subtraction: also called subtraction product, which means that each quotient is multiplied by the divisor, and the product is subtracted from the dividend.

divisor: refers to the highest digit of divisor.

product head: refers to the first digit of the product.

(4) Term 4:

Quotient head: refers to the first digit of the quotient.

quotient estimation: in division, every quotient required must be calculated by heart, and the dividend is estimated to be several times of the divisor. This mental calculation process is called quotient estimation.

trial quotient: also known as initial quotient, refers to the quotient that is too large or too small when estimating quotient, which is called trial quotient.

buy quotient: also called establish quotient, which refers to putting the trial quotient into the abacus.

Quotient adjustment: after placing the quotient, it is proved by multiplication and subtraction that the trial quotient is incorrect and the initial quotient needs to be adjusted.

exact quotient: after placing the quotient, it is proved by multiplication and subtraction that the trial quotient is neither too big nor too small.

division: it refers to dividing the dividend by the divisor, and dividing to a certain place, there is just no remainder, which is called division.

not divisible: refers to the division that cannot be divisible when there is an infinite cycle or an acyclic decimal. Such as: 1÷3=.333? ; 1÷7=.142857142857? .

(5) Term 5:

Remainder: division that is not divisible. When the quotient reaches each digit or a predetermined digit, the number remaining in the dividend is called remainder. In the process of operation, there is always a residual number in every product of quotient and divisor in the suburbs of dividend, which is usually called remainder.

business withdrawal: the initial business is too big, so change it to "business withdrawal".

complementary quotient: the initial quotient is too small, so call it complementary quotient instead.

false quotient: in the division operation, in order to calculate conveniently, a quotient is established first, and then the exact quotient is obtained through adjustment. The first established quotient is called false quotient.

liquidation: it is called liquidation to remove the counting beads from each stall and make the whole stall empty.

overall exercise: doing the ball-plucking exercise on all files or most files of the abacus, and doing the overall exercise according to the basic algorithm are called overall exercises.

Baidu Encyclopedia-abacus

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