What is the abacus formula? Thank you

The 26 mantras of abacus are as follows:1. Abacus formula table addition formula:

1. One up, one five to four, one to nine into one.

2, two on two, two down five to three, two to eight into one.

3. Three on three, three on five, three on seven, three on seven.

4. Four on four, four under five to one, four to six into one.

5, five on five, five to five into one.

6, six on six, six to **one, six on one to five into one.

7, seven on seven, seven to three into one, seven on two to five into one.

8, eight on eight, eight to two into one, eight on three to five into one.

9, nine on nine, nine to one into one, nine on four to five into one.

Second, the abacus formula table subtraction formula:

1. One down, one on four to five, one back to nine.

2. Two down two, two up and three to five, two back and one to eight.

3. Three down three, three up and two to five, three back and one to seven.

4. Four under four, four on one to five, four back to six.

5. Five under five, five back and one back five.

6, six under six, six back one to four, six back one back to five to one.

7, seven down seven, seven back one to three, seven back one back five to two.

8, eight down eight, eight back one to two, eight back one back five to three.

9, nine under nine, nine back one to one, nine back one back to five to four.

1. One up.

One, two. Two, three.

Three, four. Fourth, five.

Five, six. Six, seven.

Seven, eight. Eight, nine on nine;

2. Go to two and five.

Three, three, five go.

Two, four down five to one;

3. Go to nine in.

One, two go and eight in.

One, three to seven in.

One, four to six in.

One, five to five in.

One, six to **.

One, seven go three in.

One, eight to two in.

One, nine to one into one;

4. Six go one and five go in.

One, seven up, two go five.

One, eight up, three go, five in.

One, nine on four, five into one;

5. Take a look. One, two.

Two, three down. Three, four times.

Four, five times. Five, six.

Six, seven. Seven, eight.

Eight, nine under nine;

6. One up and four out.

Five, two up and three go.

Five, three up and two go.

Five, four, one to five;

7. One return and one return.

Nine, two return and one return.

Eighth, three retreats and one return.

Seventh, four retreats and one return.

Sixth, five return and one return.

Five, six return and one return.

Fourth, eight retreats and one return.

Second, nine back one back one;

8. Six retreats, one returns, and five goes.

One, seven retreats, one return five.

Second, eight retreats and one return five.

Three, nine back one back five go four.

Abacus mental arithmetic according to the different operations of addition, subtraction, multiplication and division have different formulas, taking the abacus mental arithmetic addition formula as an example, its content is: one up.

One, two. Two, three.

Three, four. Fourth, five.

Five, six. Six, seven.

Seven, eight. Eight, nine on nine; Two down and five go.

Three, three, five go.

Two, four down five to one; One goes nine in.

One, two go and eight in.

One, three to seven in.

One, four to six in.

One, five to five in.

One, six to **.

One, seven go three in.

One, eight to two in.

One, nine to one into one;

Mental arithmetic formula.

1. Abacus mental arithmetic addition formula table:

One on. One, two.

Two, three. Three, four.

Fourth, five. Five, six.

Six, seven. Seven, eight.

Eight, nine on nine; Two down and five go.

Three, three, five go.

Two, four down five to one;

One goes nine in. One, two go and eight in.

One, three to seven in.

One, four to six in.

One, five to five in.

One, six to **.

One, seven go three in.

One, eight to two in.

One, nine to one into one;

2. Abacus mental arithmetic subtraction formula table:

One time. One, two.

Two, three down. Three, four times.

Four, five times. Five, six.

Six, seven. Seven, eight.

Eight, nine under nine; One up and four up.

Five, two up and three go.

Five, three up and two go.

Five, four, one to five;

One return and one return. Nine, two return and one return.

Eighth, three retreats and one return.

Seventh, four retreats and one return.

Sixth, five return and one return.

Five, six return and one return.

Fourth, eight retreats and one return.

Second, nine back one back one;

3. Mental arithmetic division of the nine-return formula:

Every one into one, every two into two, every three into three, every ** four, every five into five, every six into six, every seven into seven, every eight into eight, every nine into nine.

Fourth, the abacus mental arithmetic division withdrawal formula:

No removal and retreat is one, no removal is two, no removal is three, no removal is four, no removal is five, no removal is six, no removal is seven, no removal is eight, and no removal is nine.

Fifth, the nine formulas of mental arithmetic division and quotient:

See one without division for ninety-one, see two without division for ninety-two, see three without division for ninety-three, see four without division for ninety-four, see five minds and non-division for ninety-five, see six without division for ninety-six, see seven without division for ninety-seven, see eight without division for ninety-eight, see nine without division for ninety-nine.

Straight to add five to ten plus break five into ten.

Add two: two on two, two on five, two on five, two on eight, into one.

Plus three: three on three, three down five to two, three to seven into one.

Add four: four on four, four down five to one, four to six into one.

Add five: five on five, five to five into one.

Add seven: seven on seven, seven on three, seven on two, five into one.

Add eight: eight on eight, eight on two, eight on three, five into one.

Add nine: nine on nine, nine on one into one, nine on four to five into one.

A total of 26 sentences, the first number in each sentence formula indicates the number to be added, "up", "down", "go" means to dial the beads in this file, and "in" means to carry the beads to the left gear. Addition formulas can be divided into four categories: (1) Direct addition.

That is, the addition is directly added in this file, and the abacus that has been leaning on the beam is not changed. Just dial the beads against the beam according to the number of additions. Its mantra is one to nine on nine.

2) Make up five plus. That is, the lower beads of this file are not enough, and the upper beads need to be used, and the extra number is subtracted from the lower beads. The mantra is as follows:

Two, five, three, etc. (3) Entering the ten plus. When the sum of the two numbers is full of 10 or greater than 10, the upper and lower beads of this file are not enough, and the complement of the added number is dialed in this file, and the left file is further one, and its formula is as follows:

One goes to nine into one and so on. (4) Break five into ten plus. The sum of the two numbers is more than 10, when carrying, the beads under this file are not enough, the number of "to nine", it is necessary to contact the method of breaking five in the subtraction formula, dial the upper bead, add the lower bead, and then advance one to the left.

The four operations of abacus are completed with a set of formulas to guide the completion of the beads. Addition and subtraction, the Ming Dynasty called "the upper method" and "the retreat method", its formula is unique to the abacus, first seen in Wu Jing's "Nine Chapters of Algorithm Analogy" (1450). The "ninety-nine" formula used in multiplication originated very early and was used in calculations during the Spring and Autumn Period and the Warring States Period.

Shen Kuo, a scientist in the Northern Song Dynasty, introduced the "increase method" in the eighteenth volume of his "Mengxi Writings": "Only the increase into one method is slightly different, and its technique does not need to be multiplied and divided, but it is only a profit if you make up for the loss." If you want to divide by nine, you will increase by one, and if you want to divide by eight, you will increase by two, but one person will be one because of it."

Nine dividers add one", which later became "nine plus one", and "eight dividers add two" later became "eight plus two" and other formulas. It can be seen that the "addition method" is the predecessor of the "reduction and division method". Yang Hui described the "Nine Returns" in "Multiplication and Division", and he added 32 new formulas to the four "ancient brackets" that circulated at that time, which are close to today's formulas.

Zhu Shijie's Enlightenment of Arithmetic (1299, vol. 1) of the Yuan Dynasty contains 36 sentences of the Nine Returns formula, which is roughly the same as the mantra commonly used today. In the 14th century, Ding Juju wrote eight volumes of algorithms (1355), which contained the "Recipe for Collision and Return". In short, the entire attribution formula was completed in the Yuan Dynasty.

With the four formulas, the abacus algorithm formed a system that has been used for a long time.

The formula table for abacus is as follows:Two: two on two, two down five to three, two to eight into one.

Three: three on three, three down five to two, three to seven into one.

Four: four on four, four down five to one, four to six into one.

Five: Five on five, five on five, five on five.

Seven: Seven on seven, seven on three, seven on two, five into one.

Eight: Eight on eight, eight to two into one, eight on three to five into one.

Nine: Nine on nine, nine on one into one, nine on four to five into one.

The abacus formula is as follows: 1. One up, one five to four, one to nine to one; 2, two on two, two down five to three, two to eight into one. 3. Three on three, three on five, three on seven, three on seven. 4, four on four, four down five to one, excited to do four to six into one; 5, five on five, five to five into one. 6, six on six, six to **one, six on one to five into one. 7, seven on seven, seven to three into one, seven on two to five into one. 8, eight on eight, eight to two into one, eight on three to five into one. 9, nine on nine, nine to one into one, nine on four to five into one.

Bead dialing method: one-finger bead dialing, thumb dialing down the bead against the beam, index finger dialing down the bead from the beam, dialing the bead against the beam and off the beam. The method of plucking the beads is the same for the left and right hands.

The abacus is one from right to left, ten, hundred, thousand, and ten thousand. There are two beads on the abacus and five beads on the bottom. A bead on five, a bead on ten.

Straight to add five to ten plus break five into ten.

Add two: two on two, two on five, two on five, two on eight, into one.

Plus three: three on three, three down five to two, three to seven into one.

Add four: four on four, four down five to one, four to six into one.

Add five: five on five, five to five into one.

Add seven feet buried: seven on seven, seven to three into one, seven on two to five into one.

Add eight: eight on eight, eight on two, eight on three, five into one.

Add nine: nine on nine, nine on one into one, nine on four to five into one.