Swipoa or better known as "abacus" (with suanpan or Chinese swipoa as the most helpful model) is a simple calculation tool that is still used throughout the world. It is a useful study tool for those with visual impairments, as well as anyone who wants to learn about the origins of the modern calculator. After learning the basics of counting using Swipoa, you can quickly perform arithmetic operations such as addition, subtraction, multiplication, and division.
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Part 1 of 4: Counting Using Swipoa
Step 1. Place the swipoa in the right position
Each column (or “pole”) in the top row has one or two beads, while the column in the bottom row has four beads. At the beginning of use, all the beads in the top row must be raised, and the beads in the bottom row must be lowered. In the top row, the beads have a value or equivalent to the number “5”, while in the bottom row, each bead has a value of “1”.
Step 2. Assign a place value to each column
As in modern calculators, each column has a "place value" that you use to form numbers. The rightmost column has the value "ones" (1-9), the second column from the right has the value "tens" (10-99), the third column from the right has the value "hundreds" (100-999), and so on.
- You can also assign decimal places if necessary in the column.
- For example, if you want to “form” the number “10, 5” using swipoa, the rightmost column has the value of tenths (one decimal place), the next column is the ones, and the third column has the tens value.
- As in the example above, to represent the number “10, 25”, use the rightmost column for two decimal places (hundreds), the second column from the right for one decimal place, the third column for the ones, and the fourth column for the tens.
Step 3. Start by counting the beads in the bottom row
To count a number, raise one bead to the “up” position. The number “1” is represented by raising one bead in the bottom row in the far right column to the “upper” position. The number "2" is represented by raising the two beads in the bottom row in the rightmost column to the "upper" position, and so on.
It will be easier for you to use your thumb to move the beads in the bottom row, and your index finger to move the beads in the top row
Step 4. Switch from “4” to “5”
Since there are only four beads in the bottom row, to move from the number “4” to the “5”, lower the bead in the top row to the “bottom” and return the four beads in the bottom row to their original (bottom) position. Currently, swipoa displays the number “5”. If you want to count the child "6", simply move up one bead from the bottom row to the top. At this stage, the beads in the top row are on the “bottom” (representing the number “5”) and one bead in the bottom row is on the “top” (representing the number “1”) so “5 + 1 = 6”.
Step 5. Repeat the bead removal pattern for larger numbers
The process is basically the same for every Swipoa. After the number "9" (in the ones column, all the beads in the bottom row are raised and the beads in the top row are lowered), if you want to move to the number "10", simply move one bead in the bottom row of the tens column upwards. However, return the beads in the units column to their original or “0” position.
- For example, to display the number "11" on a swipoa, increase one bead in the bottom row of the second column from the right (tens) and one bead in the bottom row of the far right column (ones). For the number "12", increase one bead in the bottom row of the tens column and two beads in the bottom row of the ones column.
- For the number "226", increase the two beads in the bottom row of the third column from the right (hundreds) and the two beads in the bottom row of the second column. In the far right column (first column or units), increase one bead in the bottom row and decrease the bead in the top row.
Part 2 of 4: Adding and Subtracting Numbers
Step 1. Enter the first number
Say you need to add up “1.234” with “5678”. Display the number "1.234" on the swipoa by raising four bottom row beads in the units column, three bottom row beads in the tens column, two bottom row beads in the hundreds column, and one bottom row beads in the thousands column.
Step 2. Start the addition from the left
The first numbers you need to add are the “1” and “5” from the thousands position. To add them up, drop the top row bead in the thousands column to add a “5” and don't move the bottom row bead so you now get a “6”. To add “2” with “6” in the hundreds place, lower the bead in the top row and increase one more in the bottom row until you get an “8” (because “5 + (2 + 1) = 8”).
Step 3. Complete the addition and displacement of the beads
Since adding the two numbers in the tens position results in the number “10”, bring the “1” from “10” into the hundreds column so that the number in the column changes from “8” to “9”. After that, return all the beads in the tens column to their original place so that the column becomes “0”.
In the units column, you also need to follow the same process. Since “8 + 4 = 12”, move the number “1” from “12” to the tens column so that in that column you have the number “1” and only “2” is left in the units column
Step 4. Add up the beads to get the answer
Now, you have a “6” in the thousands column, a “9” in the hundreds column, a “1” in the tens column, and a “2” in the ones column. This means, “1.234 + 5,678 = 6,912”.
Step 5. Perform subtraction by reversing the addition process
Instead of carrying or moving numbers, “borrow” numbers from the previous column (the column on the left side). Say you need to subtract “932” by “867”. Enter “932” into swipoa, then start the subtraction per column, starting on the left side.
- In the hundreds column, “9 – 8 = 1”. This means that there is only one bead left in the column.
- In the tens column, you can't subtract “3” from “6” so you need to borrow “1” from the hundreds column (the column is now “0”). This means that you now need to subtract “13” from “6” to get a “7” in the tens column (lower the top row bead and increase the bottom row bead two).
- Do the same for the units column by borrowing a bead from the tens column (7 – 1 = 6) so that the subtraction becomes “12 – 7” instead of “2 – 7”.
- In the units column, you will get “5”. Overall, the subtraction yields “932 - 867 = 65”.
Part 3 of 4: Multiplying Numbers
Step 1. “Save” the questions in swipoa
Start with the leftmost column first. Say you need to multiply "34" by "12". You need to assign the values “3”, “4”, “X”, “1”, “2”, and “=” to each column, starting from the left. Leave the rightmost columns for the multiplication answers.
- The symbols “X” and “=” are represented by empty columns.
- For this example, increase three bottom row beads in the leftmost column and four bottom row beads in the second column from the left, then clear the next column. After that, raise one bottom row bead in the fourth column from the left and two bottom row beads in the fifth column from the left, then empty the column next to it. Leave the other columns open or empty as space for the multiplication answer.
Step 2. Multiply the columns alternately
In multiplication, order is important. You need to multiply the first column of the first number (“3”) by the first column of the second number (“1”) after the column of crosses (“X”), then the first column of the first number (“3”) by the second column of the second number “2”). After that, multiply the second column of the second number before the cross (“4”) by the first column of the second number (“1”), then the second column of the first number (“4”) by the second column of the second number (“2”).
If you must multiply a larger number, use the same pattern. Start with the leftmost digit or column and gradually multiply to the right
Step 3. Save the multiplication answers in the proper order
Start with the first answer column which is right next to the equals column (“=”). Move the beads on the right side of the swipoa as you multiply each digit. For the question "34 x 12":
- Multiply “3” by “1” first and save the answer in the first answer column. Raise the three bottom row beads in the seventh column from the left.
- Next, multiply “3” by “2” and save the answer in the eighth column from the left. Lower the top row of beads and increase one bottom row of beads.
- When multiplying “4 x 1”, add the result of the product (“4”) to the eighth column (second answer column). Since there is already a “6” in that column and you have to add it up with “4”, bring or move one bead to the first answer column so you have a “4” in the seventh column (increase the four bottom row beads to the center of the swipoa) and “0” in the eighth column (return all beads to their original position-raise the top row bead and lower all the bottom row bead).
- Save the product of the last two digits (“4 x 2 = 8”) in the last answer column. Now, the answer columns display the numbers “4”, “0”, and “8” so the final multiplication result is “408”.
Part 4 of 4: Dividing Numbers
Step 1. Leave space for the answer to the right of the divisor, before the number is divided
When dividing using swipoa, place the divisors in the leftmost columns. Leave a few blank columns on the right side, then place the divided numbers in the following columns. The rest of the column on the right side of swipoa will be used to search for answers. For now, leave these fields blank.
- For example, to divide “34” by “2”, place “2” in the leftmost column, leaving two blank columns next to it, then add “34” to the right. Leave the other columns blank for the division answer.
- To divide a number, increase the two bottom row beads in the leftmost column. Leave the two columns next to it. In the fourth column from the left, raise the three bottom row beads. In the fifth column, raise four bottom row beads.
- The empty fields between the divisor and divide are used to separate the numbers so you don't get confused.
Step 2. Save the quotient
Divide the first digit in the divisible number (“3”) by the divisor (“2”) and enter the answer in the first answer column. The number "2" can only be multiplied once so that the result is equal to or close to "3" so enter "1" in the first answer column.
- To enter the number "1", increase the bottom row of beads in the first answer column.
- If you want, you can skip a column (leave it blank) between the divided numbers and the answer column. This way, you can tell the difference between a divided number and the result of a division.
Step 3. Determine the remainder
After that, you need to multiply the quotient in the first answer column (“1”) by the divisor in the leftmost column (“2”) to find the remainder. The result of the multiplication (“2”) is used to subtract the first column of a divisible number (“3” from “34”). Now, the number is divided into “14”.
In order for Swipoa to display the number “14” as a divisible number, lower the two bottom row beads on the fourth bar (or fifth if you use an empty column after the divisor column) that has been raised to the initial position. Only one of the bottom row beads in the column remains in the top position (near the center bar of the divider)
Step 4. Repeat the same process
Enter the next quotient in the next answer column and subtract the number divided by that result (in this case, delete it). Now, swipoa displays the number “2”, followed by a blank column (if you use it as a separator), “1”, and “7”. The numbers are the divisor (“2”) and the final result of the division (“17”).
- The bottom two row beads in the far left column must be raised to the center bar of the swipoa.
- The leftmost column is followed by several blank columns as separators (if you use separators).
- One bottom row bead in the first answer column must be raised.
- In the next answer column, two bottom row beads are raised and the top row beads are lowered.
