Using an Abacus
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An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It is still widely used by merchants and clerks in the China, Japan, Hong Kong, Africa, and elsewhere. This guide currently explains how to use the Chinese abacus.
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[edit] Basics
See also: Abacus on Wikipedia
Using an abacus consists of memorizing 'secrets' so that you don't have to think while using it. When well practiced, high speed is achievable. The secrets for addition and subtraction consist of memorized bead movements on each digit based upon number of active beads, value of the number, and adding or subtracting. The secrets of multiplication and division consist of the addition/subtraction secrets and the multiplication table.
[edit] Value
An abacus is placed so that the side with five beads is toward you and the side with two beads is away from you. Each bead on your side has a value of 1, and each bead on the other side has a value of 5. The value of a digit is based upon the number of beads that are next to the center bar.
The full number is by decimal place system, right column being the least significant. If you had a three column abacus, and the left most column had a 1 bead next to the bar and the middle column had a 5 bead next to the bar and the right most column had one of each, the number is one hundred fifty six (156).
Abacuses can also represent fractional amounts. The position of the decimal point must be memorized.
Some abacuses have a dot on the bar for every third column. This greatly aids in remembering which column represents each decimal place. The column representing numbers less than ten (ones) typically is one of the columns with a dot on the bar.
[edit] Secrets
A secret will be in the form of 0-3,5-8: move 1 bead up. 0-3,5-8 means if the current digit on the abacus has a value of 0, 1, 2, 3, 5, 6, 7, or 8.
Each secret should be practiced so that you can perform the motion without thinking about it. Since you are training your fingers, use a real abacus. Using a miniature one will require re-training if you switch, although the re-training will be easier than learning for the first time.
[edit] Addition
Add 1
This set of secrets is the most important because the others rely on it for carrying.
0-3,5-8: move 1 bead up.
4: move a 5 bead down with 4 beads. In your practice this means that you should place your fingers so that you can move the 5 bead down while moving the other beads down at the same time - increasing your speed of calculation.
9: add 1 to next column and remove all beads. In your practice this means that you use this set of secrets while using two other fingers (thumb and pinkie worked for me) to remove beads.
Add 2
0-2,5-7: move 2 beads up.
3-4: move a 5 bead down with 3 beads.
8-9: add 1 to next column and separate a 5 and 3 beads. In your practice this means that you use the add 1 secrets while using two other fingers to remove a 5 bead and three 1 beads at the same time.
Add 3
0-1,5-6: move 3 beads up.
2-4: move a 5 bead down with 2 beads.
7-9: add 1 to next column and separate a 5 and 2 beads.
Add 4
0,5: move 4 beads up.
1-4: move a 5 bead down with 1 bead.
6-9: add 1 to next column and separate a 5 and 1 bead.
Add 5
0-4: move a 5 bead down.
5-9: add 1 to next column and separate a 5 bead.
Add 6
0-3: move a 5 and 1 bead together. In your practice, the beads should come together in one smooth motion.'
4: add 1 to the next column and remove 4 beads. Remember, at the same time and smoothly.
5-8: add 1 to the next column and move a 5 and 1 bead up. Move them up together at the same time as adding 1 to the next column. If you can't do them together, practice the add 1 secrets more.
9: add 1 to next column and bring the 4 beads down.
Add 7
0-2: move a 5 and 2 beads together.
3-4: add 1 to the next column and remove 3 beads.
5-7: add 1 to the next column and move a 5 and 2 beads up.
8-9: add 1 to next column and 3 beads down.
Add 8
0-1: move a 5 and 3 beads together.
2-4: add 1 to the next column and remove 2 beads.
5-6: add 1 to the next column and move a 5 and 3 beads up.
7-9: add 1 to next column and 2 beads down.
Add 9
0: move a 5 and 4 beads together.
1-4: add 1 to the next column and remove 1 bead.
5: add 1 to the next column and move a 5 and 4 beads up.
6-9: add 1 to next column and 1 bead down.
[edit] Practice
1: Pick a secret to practice. Set your abacus up to the number 123456789. Perform the secret from the right column to the left. 2: Pick a secret to practice. Set your abacus up to the number 987654321. Perform the secret from the right column to the left. 3: Pick a secret to practice. Pick a number to practice. Set every digit of your abacus to the number. Perform the secret from the right column to the left column. 4: Pick a secret to practice. Shake your abacus, adjust beads to be definite, perform the secret for each column from the right to the left.
[edit] Subtraction
[edit] Multiplication
The secrets of this consist of the Multiplication Table for 0 times 0 up to 9 times 9.
[edit] Division
Trying to remember if there was a further secret.
[edit] Operations
[edit] Addition
Addition is easy. Simply follow these steps.
- Choose the point of the decimal place.
- Put one of the numbers on your abacus.
- Perform the addition secrets for the other number from right to left.
- Read off the result.
Example: 12.5 + 3.75
- Because the most decimal places we have in a number we're working with is two, we choose to use two decimal places.
- We decide to put 12.5 on the abacus so in the column 4th from the right, we place 1 because of where our decimal point is. In the next column, we place 2. In the next column, we place 5. In the next column, we place 0 (12.50).
- We perform the add 5 secret to the rightmost column (12.55). We perform the add 7 secret for the previous column (13.25). We perform the add 3 secret for the previous column (16.25).
- Read off the result of 16.25.
If we have a series of addition to perform, then step 1 is skipped (since it is already there).
If you find you need to change your decimal point, it is easy enough to move numbers right or left one digit at a time.
If you don't have enough digits, place two abacuses side by side. The only part of the calculation which should slow you down is carrying or borrowing across abacuses.
[edit] Subtraction
This is simple.
1 Choose the point of your decimal place.
2 Put one of the numbers on your abacus.
3 Perform the subtraction secrets for the other number from left to right.
4 Read off your result.
[edit] Multiplication
1 If the numbers involved are decimals, count how many digits behind the decimal there is total for both numbers.
2 Set your abacus to one of the numbers
3 Add that number to itself for the number in that starting place.
4 Read your answer Example: 12.5 × 48
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[edit] Division
Need to refresh my memory.
[edit] Square root
Any information useful.
[edit] Cube root
Any information useful.
see [1]
[edit] External links
- Abacus: Mystery of the Bead - An Abacus Manual
- Advanced Abacus Techniques
- Lee Kai-chen's Improved Abacus - A demonstration of how the Lee's Abacus works
