The abacus (suanpan is the most useful variety), is a calculation tool that looks simple and is still used around the world. It is a useful learning device for the visually impaired and anyone who wants to learn the origins of the modern calculator. Once you learn the basics of using an abacus, you can quickly do math like addition, subtraction, multiplication, and division.
Part 1 of 4: Counting
Step 1. Orient the abacus correctly
Each column in the top row must have one or two beads per row, while each column in the bottom row must have four beads. At the beginning, all accounts must be in the top and bottom row. The beads in the upper row represent the number 5, and each bead in the lower row represents the number 1.
Step 2. Give each column a house
As in the modern calculator, each column of accounts represents a house, from which a number is assembled. Therefore, the rightmost column would be the units (1-9), the second-rightmost column, the tens (10-99), the third, the hundreds (100-999), and so on.
- You can also assign some columns to decimal places if needed.
- For example, to represent a number like 10, 5, the rightmost column would be the first decimal place; the second, the unit house; and the third, the tens place.
- Likewise, to represent a number such as 10, 25, the rightmost column would be the second decimal place; the second column would be the first decimal place; the third would be that of units, and the fourth, that of tens.
Step 3. Start counting the bottom row accounts
To count a digit, push a bead up. The number one is represented by pushing a single bead from the bottom row of the rightmost column up. For two, push two accounts, etc.
You will find it easier to use your thumb to move the beads in the upper row, and your index finger to move the beads in the lower row
Step 4. Complete the 4 to 5 switch
Since there are only four beads in the bottom row, to move from 4 to 5, push the top row bead down and all four bottom row beads down as well. The correct abacus reading at this position is 5. To count 6, push a bead from the bottom row to the top so that the bead from the top row is down (representing the value 5), and a bead from the bottom row is to up.
Step 5. Repeat pattern for larger numbers
The process is essentially the same throughout the abacus. Go from 9, where all unit accounts are up and the top row count will be down, to 10, where a lower tens place count is pushed up, while the tens place counts are pushed up. units are pushed back to the starting position.
- For example, 11 would have a count from the second column on top, and one from the first column also up, all from the bottom row. The 12 would have one in the second column and two in the first column, all up, and all in the bottom row.
- 226 would have two beads from the third column pushed up on the bottom row, and two from the second column also pushed up on the bottom row. In the first column, a count from the bottom row would be up, and the count from the top row would be down.
Part 2 of 4: Adding and Subtracting
Step 1. Enter the first number
Let's say you need to add 1234 + 5678. Put 1234 on the abacus by pushing up four beads from the ones place, three out of the tens, two out of the hundreds, and one out of the thousands.
Step 2. Start adding from the left
The first numbers to be added are the 1 and 5 of thousands, in this case moving the single count from the top row of that column down to add the 5, and leaving the bottom count up, totaling 6. In the same way, to add 6 to the hundreds place, move the top hundreds place count down, and one bottom row count up, for a total of 8.
Step 3. Complete an exchange
Since the sum of the two numbers in the tens place will result in a 10, you will move the 1 to the hundreds place, making a 9 in that column. Then lower all the accounts in the tens place, leaving it at zero.
Do the same thing in the units column. 8 + 4 = 12, so pass the 1 to the tens place, making the 1 in it. You will get the 2 in the unit house
Step 4. Count the accounts to find the answer
You got a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the units: 1234 + 5678 = 6912.
Step 5. Subtract by doing the addition process in reverse
Borrow digits from the previous column instead of passing them forward. Let's say you're subtracting 867 from 932. After entering 932 into the abacus, subtract column by column, starting from the left.
- 9 - 8 = 1, so leave an account in the hundreds place.
- In the tens place, you cannot subtract 6 from 3, so borrow 1 from the hundreds place (leaving it at zero) and subtract 6 from 13, making the tens result equal to 7 (a top count down and two lower ones upwards).
- Do the same in the units square, borrowing a tens account (which turns into 6) to subtract 7 from 12 instead of 2.
- There will be a 5 in the units column: 932 - 867 = 65.
Part 3 of 4: Multiplying
Step 1. Record the problem on the abacus
Start with the leftmost column of it. Let's say the count is 34 x 12. You need to assign columns to 3, 4, x, 1, 2 and =. Leave the other columns on the right free for the product.
- The x and the = will be represented by blank columns.
- The abacus should have three beads up in the leftmost column, four beads up in the second leftmost column, one blank column, one column with one bead up, two beads up in the next, and another blank column. The rest of the columns are free.
Step 2. Multiply by alternating columns
The order here is critical. You need to multiply the first column by the first column after the one that is blank, and then the first column by the second column after the one that is blank. Next, you will multiply the second column by the first column after the one that is blank, and finally, the same second column by the second column after the one that is blank.
If you're multiplying larger numbers, keep the same pattern: start with the leftmost numbers and work your way to the right
Step 3. Register the products in the correct order
Start recording in the first answer column, after the one that was left blank to represent the =. You will move the beads to the right of the abacus as you multiply the individual digits. For the 34 x 12 problem:
- First, multiply 3 by 1 and record the product in the first answer column. Push three beads up in the seventh column.
- Then multiply the 3 and the 2, recording the product in the eighth column. Push one bead from the top section down, and one bead from the bottom section up.
- When you multiply the 4 and the 1, add that product (4) to the eighth column, the second column of answers. Since you're going to add the 4 to a 6 in that column, take a bead to the first answer column, leaving it with a 4 (four beads from the bottom section pushed up to the center bar) and a 0 in the second column (All beads in original positions: top section up and bottom section down).
- Record the product of the last two digits, 4 and 2 (8), in the last answer column. You will now have 4, blank column, and 8, which represents answer 408.
Part 4 of 4: Dividing
Step 1. Leave space for the answer to the right of the divisor and dividend
When splitting on an abacus, you place the splitter in the leftmost columns. Leave some columns blank on the right and place the dividend in the columns next to them. The remaining columns on the right will be used to make the count that will lead to the answer. Leave them blank for now.
- For example, to divide 34 by 2, count 2 in the leftmost column, leave two blank, and place 34 on the right. Leave the other columns blank to enter the answer.
- To form the numbers, push two beads from the bottom up in the leftmost column. Leave the next two columns blank. In the fourth column, push three beads from the bottom to the top. In the fifth column from the left, push four beads from the bottom to the top.
- The blank columns between the divisor and the dividend are just for visually separating the numbers, so you don't get confused.
Step 2. Record the quotient
Divide the first number of the dividend (3) by the divisor (2) and place the result in the first blank column of the answers part. It fits a 2 in 3, so put the 1 there.
- To do this, push a bottom bead up in the first column of the answer part.
- If you like, you can skip a column (leave it blank) between the dividend and the columns you want to use for the answer. This will help you separate between the dividend and the calculation.
Step 3. Determine the rest
Next, you need to multiply the quotient in the first column of the answer (1) by the dividend in column one (2) to know what the remainder of the division is. This product (2) needs to be subtracted from the first column of the dividend. The dividend will now represent 14.
To make the dividend represent 14, push two bottom beads that are up in the fifth column back to the starting position. Only one bead from the bottom of the fifth column must stand against the center bar
Step 4. Repeat the process
Write the next digit of the quotient in the next blank column of the answer part, subtracting the product of the dividend (eliminating it in this case). The abacus will now indicate a 2 followed by blank columns, then 1 and 7, showing the divisor and quotient, 17.
- Two beads from the bottom of the leftmost column will be against the center bar.
- They will be followed by several blank columns.
- A count from the bottom of the first column of the answer will be against the center bar.
- In the next column of the answer, two beads from the bottom will be against the center bar, and the bead from the top will be pushed down against the bar.