Content

• Steps
• Part 1 of 4: Counting Basics
• Part 2 of 4: Addition and Subtraction
• Part 3 of 4: Multiplication
• Part 4 of 4: Division
• Tips

Abacus is a seemingly simple calculation tool that is still used all over the world today. It is a useful device for educating people with visual impairments, as well as for anyone who wants to get to know the historical roots of the modern calculator. After reading this article, you will learn how to perform calculations using counting.

Steps

Part 1 of 4: Counting Basics

1. 1 Turn the abacus right. Regular abacus consists of two rows of beads, grouped into columns, the number of which can vary. Each column in the top row contains one or two beads, while each column in the bottom row should have four beads. When you start calculating, all the beads in the top row should be up and the beads in the bottom row should be at the bottom. The beads in the top row are assigned a value of 5, and each bead in the bottom row is assigned the number 1.
   • Once you become more familiar with the counting functions, you can assign different values ​​to the beads in the bottom row to do more complex calculations. The beads in the top row, however, need to be 5 times larger than the beads in the bottom row for the counting method to work.
2. 2 Assign a numeric digit to each column. Just like a modern calculator, each column of beads represents a digit from which you begin to compose a number. So, the rightmost column will be the ones (1-9), the second row from the right will be tens (10-99), the third from the right will be hundreds (100-999), and so on.
   • Depending on your calculations, you can also add decimal positions that you will track. If you want to dial the number 12,345.67, the number 7 will be in the first column, 6 in the second, 5 in the third, and so on.When calculating, just remember where the decimal position is by marking it on the abacus with a pencil, or skip the row and leave it blank.
3. 3 Start typing a number. To enter a number, move one bead up. "One" is indicated by moving one bead of the bottom row in the rightmost column upward, "two" by moving two beads, and so on.
4. 4 Replace 4 by 5."Since there are only four beads in the bottom row, to go from four to five, you need to move the top row down and move down all four of the bottom row as well. The abacus in this position reads correctly as' five. 'To enter' six ", move one bead from the bottom row up, so the bead from the top row is at the bottom (denoting" five "), and one bead from the bottom row is at the top.
   • This principle is practically the same for all categories of the account. Go from position "nine", in which all the beads in the first row are moved up, and the bead in the top row is at the bottom, to "ten", when the only bead in the lower row of the second category is lifted.
   • Here is an example: the number 12345 will be composed of one bead of the top row in the rank of ones, four raised beads of the bottom row in tens, three raised beads of the bottom row in hundreds, two beads of the bottom row in thousands, and one bead of the bottom row in tens of thousands.
   • You can forget to omit the beads of the lower row when changing the category, and then the board will show the wrong value. It's pretty easy to keep track of this with simple calculations, but when you move on to more complex arithmetic calculations, it becomes more difficult.

Part 2 of 4: Addition and Subtraction

1. 1 Enter the first number. Let's say you need to add 1234 and 5678. Enter 1234 in the abacus, moving up four beads in ones, three beads in tens, and so on.
2. 2 Start folding to the left. Unlike traditional arithmetic, in which you start at the first column and work your way to the left, counting works from left to right. So, the first digits you will add will be 1 and 5 in the thousand place, so move one bead of the top row of the corresponding column down to add 5, and leave one bead of the bottom row at the top to get 6. Similarly, lower the top bead of the top rows in hundreds and pick up another bead from the bottom row to get 8 in hundreds.
3. 3 Replace. It takes a little trickery here. Since adding two digits in tens will give 10, you need to translate 1 into hundreds to get 9 in a column. Next, lower all the beads down in tens, leaving zero.
   • In the ones column, you do essentially the same thing. 8 + 4 = 12, so you translate one into tens, which is 1, leaving 2 in units.
4. 4 Count the beads. You have 6 left in the thousands column, 9 in hundreds, 1 in tens and 2 in units: 1234 + 5678 = 6912.
5. 5 To subtract, follow the same procedure, but in the opposite direction. Take the numbers from the previous column instead of carrying them over. Let's say you subtract 867 from 932. After you have entered 932 in the accounts (top bead at the top and four bottom beads at the top in the column of hundreds, three bottom beads at the top in tens and 2 lower beads at the top in units), start subtracting column by column left.
   • 9 minus 8 equals 1, so leave one bead at the top in the hundreds. In tens, you cannot subtract 6 from 3, so take one in hundreds (leaving 0 there) and subtract 6 from 13 to get 7 in tens (the top bead and 2 bottom beads are at the top). Repeat the same with units, taking a bead from tens (getting 6 there) to subtract 7 from 12 instead of 2. In units it should be 5: 932 - 867 = 65.

Part 3 of 4: Multiplication

1. 1 Adapt the task to fit the score. Unlike addition, when multiplying it is best to start counting from the leftmost column. For example, you are multiplying 34 by 12. You need to set the columns to "3" "4" "X" "1" "2" "=" and leave the columns to the right of them blank for the product. You need at least three columns for this task.
   • The "X" and "=" values ​​should just be the place you leave blank to separate the numbers, so it takes six columns in the accounts to enter "34 x 12 =".
   • On accounts, you need to pick up 3 beads in the leftmost column, 4 in the next column, then an empty column, one bead up, another empty column and at least three more columns for the result of multiplication.
2. 2 Multiply alternating columns. Order is very important. You must multiply the first column by the first column after the break, then the first column by the second column after the break. Next, you multiply the second column before the space by the second column after the space. This sequence must always be followed.
3. 3 Write the piece down in the correct order. First, you multiply 3 by 1, writing the result in the first column for the answer, which in this case will be the seventh column from the left, counting every digit and every space column. Pick up the three beads in this seventh column. Then multiply 3 by 2 by writing your answer in the eighth column. Pick up the top bead and one bottom bead in this column.
   • At this stage, the difficulties begin. When you multiply 4 by 1, you need to add the result in the eighth column, which is also the second column for the answer. The product of 4 and 1 is 4, and since you are adding 4 to 6 in this column, you need to move one bead to the first column for your answer, getting 4 in the seventh column and 0 in the eighth.
   • Multiply the last two digits in the problem, 4 and 2, and record the result in the ninth column by placing 8 in the last column for the answer, which now reads 4, space, 8, making the answer 408.

Part 4 of 4: Division

1. 1 To divide numbers, leave room for the answer between the divisor and the dividend. Division is a more dynamic process than multiplication and works best when you leave no blank space between the numbers. The farthest left column of the count will be the divisor, the number divided by. The next columns on the right should be left to record the answer.
   • For example, you divide 34 by 2. You know that the answer will fit in at least 2 columns, so leave 2 columns between 2 on the right and 3 and 4.
   • So, to enter 34 divided by 2 in accounts, you must have 2 in the leftmost column, two columns for the answer, 3 in the fourth column, and 4 in the fifth.
2. 2 Write down the quotient. Take the first digit of the dividend (3) and divisor (2) in the first column for your answer. 2 goes into 3 once, so write 1 in the second column.
3. 3 Determine the remainder. Next, you need to multiply the quotient in the second column (1) by the dividend in the first column (2) to calculate the remainder. Result (2) must be subtracted from the fourth column. The divisor should now be 14.
4. 4 Repeat the procedure. Fix the next digit of the quotient in the third column by subtracting the result from the divisor (in this case, destroying it). Your account entry should read 2,1,7, leaving the dividend and quotient, 17.

Tips

• In Japanese soroban, this method works a little differently, in terms of how the columns are added and subtracted, and the "five" beads move not up, but down, but still move from left to right in the same way to perform calculations, and also work on the same principle.
• If you are working with decimal fractions, then the column of units can be moved to the left.
• If you are dealing with numbers in which the values ​​of the digits in the ones place are not important because of the magnitude of the numbers, the column of ones can be moved to the right (removed from the accounts).