How to Use an Abacus
Orient your abacus properly., Assign each column a place value., Start counting with the beads in the lower row., Complete the "4/5 exchange.” Since there are only four beads on the bottom row, to go from "four" to "five," you push the bead on the...
Step-by-Step Guide
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Step 1: Orient your abacus properly.
Each column in the top row should have one or two beads per row, while each column in the bottom row should have four.
When you start, all of the beads should be up in the top row, and down in the bottom row.
The beads in the top row represent the number value 5 and each bead in the bottom row represents the number value
1., As on a modern calculator, each column of beads represents a "place" value from which you build a numeral.
So, the farthest column on the right would be the "ones" place (1-9), the second farthest the "tens" place (10-99), the third farthest the hundreds (100-999), and so on.You can also assign some columns to be decimal places if necessary. , To count a digit, push one bead to the "up" position. "One" would be represented by pushing a single bead from the bottom row in the farthest column on the right to the "up" position, "two" by pushing two, etc.You'll find it easiest to use your thumb to move the beads in the top row, and your index finger to move the beads in the bottom row. , The abacus at this position is correctly read "five." To count "six," push one bead from the bottom row up, so the bead in the top row is down (representing a value of 5) and one bead from the bottom row is up., The process is essentially the same across the abacus.
Go from "nine," in which all the beads in the ones place are pushed up and the bead in the top row is pushed down, to "ten," in which a single bead from the bottom row of the tens place is pushed up.
For example, 11 would have one bead in the second column pushed up, and another in the first column pushed up, all on the bottom row. 12 would have one in the second column and two in the first column, all pushed up, and all on the bottom row. 226 would have two in the third column pushed up in the bottom row, and two in the second column pushed up in the bottom row.
In the first column, one bead on the bottom row would be pushed up, and one bead on the top row would be pushed down. , Say you've got to add 1234 and
5678.
Enter 1234 on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place., The first numbers you'll add are the 1 and the 5 from the thousands place, in this case moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of
6.
Likewise, to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of
8. , Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column.
Next, put all the beads down in the tens place, leaving it zero.
In the ones column, you'll do essentially the same thing. 8 + 4 = 12, so you'll carry the one over to the tens place, making it
1.
This leaves you with 2 in the ones place. , You're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the ones: 1,234 + 5,678 = 6,912. , Borrow digits from the previous column instead of carrying them over.
Say you're subtracting 867 from
932.
After entering 932 into the abacus, start subtracting column-by-column starting on your left. 8 from 9 is one, so you'll leave a single bead up in the hundreds place.
In the tens place, you can't subtract 6 from 3, so you'll borrow the 1 in the hundreds place (leaving it zero) and subtract 6 from 13, making it 7 in the tens place (the upper bead up and two lower beads).
Do the same thing in the ones place, "borrowing" a bead from the tens place (making it 6) to subtract 7 from 12 instead of
2.
There should be a 5 in the ones column: 932
- 867 =
65. , Start at the farthest left column of the abacus.
Say you're multiplying 34 and
12.
You need to assign columns to "3"
"4"
"X"
"1"
"2"
and "=".
Leave the rest of the columns to the right open for your product.The “X” and “=” will be represented by blank columns.
The abacus should have 3 beads up in the farthest column left, four up in the next farthest, a blank column, a column with one bead up, two beads up in the next, and another blank column.
The rest of the columns are open. , The order here is critical.
You need to multiply the first column by the first column after the break, then the first column by the second column after the break.
Next, you'll multiply the second column before the break by the first column after the break, then the second column before the break by the second column after the break.If you are multiplying larger numbers, keep the same pattern: start with the leftmost digits, and work to the right. , Start recording in the first answer column, after the blank one for the “=” sign.
You will keep moving beads on the right hand portion of the abacus as you multiply the individual digits.
For the problem 34 x 12:
First, multiply 3 and 1, recording their product in the first answer column.
Push three beads up in that seventh column.
Next, multiply the 3 and the 2, recording their product in the eighth column.
Push up the upper bead and one lower bead in that column.
When you multiply the 4 and the 1, add that product (4) to the eighth column, the second of the answer columns.
Since you're adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column and a zero in the eighth.
Record the product of the last two digits 4 and 2 (8), in the last of the answer columns.
They should now read 4, blank, and 8, making your answer
408. , When dividing on an abacus, you will put the divisor in the left-most column(s).
Put the dividend in the columns just to the right of this.
The next columns to the right will be used for the answer.
Leave those blank for now.For example, to divide 34 by 2, count 2 in the left-most column, and 34 over to the right.
Leave the other columns blank. , Divide the first number in the dividend (3) by the divisor (2), and put it in the first blank column on the right. 2 goes into 3 once, so record a 1 there. , Next, you need to multiply the quotient in the first answer column (1) by the dividend in column one (2) to determine the remainder.
This product (2) needs to be subtracted from the first column of the dividend.
The dividend should now read
14. , Record the next digit of the quotient in the next blank column, subtracting the product from the divisor (here, eliminating it).
Your board should now read 2, then 1, 7, showing your divisor and the quotient,
17. -
Step 2: Assign each column a place value.
-
Step 3: Start counting with the beads in the lower row.
-
Step 4: Complete the "4/5 exchange.” Since there are only four beads on the bottom row
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Step 5: to go from "four" to "five
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Step 6: " you push the bead on the top row to the "down" position and push all four beads from the bottom row down.
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Step 7: Repeat the pattern for higher numbers.
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Step 8: Input your first number.
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Step 9: Start adding from the left.
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Step 10: Complete an exchange.
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Step 11: Count your beads to get the answer.
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Step 12: Subtract by doing the addition process in reverse.
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Step 13: Record the problem on the abacus.
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Step 14: Multiply by alternating columns.
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Step 15: Record the products in the correct order.
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Step 16: Leave space for the answer to the right of the divisor and the dividend.
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Step 17: Record the quotient.
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Step 18: Determine the remainder.
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Step 19: Repeat the process.
Detailed Guide
Each column in the top row should have one or two beads per row, while each column in the bottom row should have four.
When you start, all of the beads should be up in the top row, and down in the bottom row.
The beads in the top row represent the number value 5 and each bead in the bottom row represents the number value
1., As on a modern calculator, each column of beads represents a "place" value from which you build a numeral.
So, the farthest column on the right would be the "ones" place (1-9), the second farthest the "tens" place (10-99), the third farthest the hundreds (100-999), and so on.You can also assign some columns to be decimal places if necessary. , To count a digit, push one bead to the "up" position. "One" would be represented by pushing a single bead from the bottom row in the farthest column on the right to the "up" position, "two" by pushing two, etc.You'll find it easiest to use your thumb to move the beads in the top row, and your index finger to move the beads in the bottom row. , The abacus at this position is correctly read "five." To count "six," push one bead from the bottom row up, so the bead in the top row is down (representing a value of 5) and one bead from the bottom row is up., The process is essentially the same across the abacus.
Go from "nine," in which all the beads in the ones place are pushed up and the bead in the top row is pushed down, to "ten," in which a single bead from the bottom row of the tens place is pushed up.
For example, 11 would have one bead in the second column pushed up, and another in the first column pushed up, all on the bottom row. 12 would have one in the second column and two in the first column, all pushed up, and all on the bottom row. 226 would have two in the third column pushed up in the bottom row, and two in the second column pushed up in the bottom row.
In the first column, one bead on the bottom row would be pushed up, and one bead on the top row would be pushed down. , Say you've got to add 1234 and
5678.
Enter 1234 on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place., The first numbers you'll add are the 1 and the 5 from the thousands place, in this case moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of
6.
Likewise, to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of
8. , Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column.
Next, put all the beads down in the tens place, leaving it zero.
In the ones column, you'll do essentially the same thing. 8 + 4 = 12, so you'll carry the one over to the tens place, making it
1.
This leaves you with 2 in the ones place. , You're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the ones: 1,234 + 5,678 = 6,912. , Borrow digits from the previous column instead of carrying them over.
Say you're subtracting 867 from
932.
After entering 932 into the abacus, start subtracting column-by-column starting on your left. 8 from 9 is one, so you'll leave a single bead up in the hundreds place.
In the tens place, you can't subtract 6 from 3, so you'll borrow the 1 in the hundreds place (leaving it zero) and subtract 6 from 13, making it 7 in the tens place (the upper bead up and two lower beads).
Do the same thing in the ones place, "borrowing" a bead from the tens place (making it 6) to subtract 7 from 12 instead of
2.
There should be a 5 in the ones column: 932
- 867 =
65. , Start at the farthest left column of the abacus.
Say you're multiplying 34 and
12.
You need to assign columns to "3"
"4"
"X"
"1"
"2"
and "=".
Leave the rest of the columns to the right open for your product.The “X” and “=” will be represented by blank columns.
The abacus should have 3 beads up in the farthest column left, four up in the next farthest, a blank column, a column with one bead up, two beads up in the next, and another blank column.
The rest of the columns are open. , The order here is critical.
You need to multiply the first column by the first column after the break, then the first column by the second column after the break.
Next, you'll multiply the second column before the break by the first column after the break, then the second column before the break by the second column after the break.If you are multiplying larger numbers, keep the same pattern: start with the leftmost digits, and work to the right. , Start recording in the first answer column, after the blank one for the “=” sign.
You will keep moving beads on the right hand portion of the abacus as you multiply the individual digits.
For the problem 34 x 12:
First, multiply 3 and 1, recording their product in the first answer column.
Push three beads up in that seventh column.
Next, multiply the 3 and the 2, recording their product in the eighth column.
Push up the upper bead and one lower bead in that column.
When you multiply the 4 and the 1, add that product (4) to the eighth column, the second of the answer columns.
Since you're adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column and a zero in the eighth.
Record the product of the last two digits 4 and 2 (8), in the last of the answer columns.
They should now read 4, blank, and 8, making your answer
408. , When dividing on an abacus, you will put the divisor in the left-most column(s).
Put the dividend in the columns just to the right of this.
The next columns to the right will be used for the answer.
Leave those blank for now.For example, to divide 34 by 2, count 2 in the left-most column, and 34 over to the right.
Leave the other columns blank. , Divide the first number in the dividend (3) by the divisor (2), and put it in the first blank column on the right. 2 goes into 3 once, so record a 1 there. , Next, you need to multiply the quotient in the first answer column (1) by the dividend in column one (2) to determine the remainder.
This product (2) needs to be subtracted from the first column of the dividend.
The dividend should now read
14. , Record the next digit of the quotient in the next blank column, subtracting the product from the divisor (here, eliminating it).
Your board should now read 2, then 1, 7, showing your divisor and the quotient,
17.
About the Author
James Mitchell
Dedicated to helping readers learn new skills in crafts and beyond.
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