The Chinese abacus has 13 wires on a wooden frame, with a wooden divider not quite down the middle of all the wires. Each wire has seven beads, five on one side of the division (the "earth" beads, worth one each) and two on the other (the "heaven" beads, each of which is worth five.)

The modern Japanese abacus has only one bead above the divider and four below, and usually has 21 wires.

To represent a number on the abacus, beads are moved toward the divider. The rightmost wire represents the ones, the next one over the tens; the third from the right stands for hundreds, and so on. For example, here's a diagram of a Chinese abacus showing 54,927:

```heaven beads
-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O | | |
| O O O O O O O O O O O O O |
| O O O O O O O O O | | O O |
| O O O O O O O O O O O O O |
-----------------------------
```
Note that the beads furthest away from the divider don't need to be used to represent base 10 numbers on the Chinese abacus; that's why they were able to be removed in the Japanese abacus. The extra beads help, though, when you are doing math. Also, you can use the Chinese abacus to represent (and do calculations with) numbers other than base 10. E.g., you can do binary calculations by working just with the heaven beads. You can also slide the decimal point around, and do arithmetic with fractions if you so desire.

To add numbers with an abacus, enter the first number. Suppose we wanted to calculate 54,927 + 18. Start with the bigger number:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O | | |
| O O O O O O O O O O O O O |
| O O O O O O O O O | | O O |
| O O O O O O O O O O O O O |
-----------------------------
```
Then go column by column, adding the second number to the first. It's best to work from the right to the left. There aren't enough beads in the ones column to add 8 to 54,927, so instead add one to the tens ...
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O | |
| O O O O O O O O O O O | O |
| O O O O O O O O O | | O O |
| O O O O O O O O O O O O O |
-----------------------------
```
... and take away two from the ones:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O | O |
| O O O O O O O O O | | O O |
| O O O O O O O O O O O O O |
-----------------------------
```
Now, add one to the tens column (the "1" in "18"):
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O | | | O |
| O O O O O O O O O O O O O |
-----------------------------
```
... and we are left with 54,945.

#### Subtraction

```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O | | | O |
| O O O O O O O O O O O O O |
-----------------------------
```
Subtracting 0 is a no-op; to subtract 90, first subtract 100 ...
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | O | |
| | | | | | | | | O | O | O |
-----------------------------
| | | | | | | | | | O O O | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O | O O |
| O O O O O O O O O | O | O |
| O O O O O O O O O O O O O |
-----------------------------
```
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | | | |
| | | | | | | | | O | O O O |
-----------------------------
| | | | | | | | | | O O | | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O | O O |
| O O O O O O O O O | O O O |
| O O O O O O O O O O O O O |
-----------------------------
```
Now, subtract 200 to get the answer (54,655)
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O | O | | | |
| | | | | | | | | O | O O O |
-----------------------------
| | | | | | | | | | O O | | |
| O O O O O O O O O O | O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O | O O O |
| O O O O O O O O O O O O O |
-----------------------------
```

#### Multiplication

To perform multiplication with an abacus, basically you perform addition repeatedly. In order to keep track of how many times you have added the number, you can use one of the unused leftmost columns of beads. This works well with smaller numbers. If you want to multiply numbers that have multiple digits, then memorize your multiplication table and do it like you would on paper. E.g., 37 times 23 would be 21 + 90 + 140 + 600.

#### Division

Division can be performed as repeated subtraction, using one of the leftmost columns to keep track of how many times the subtraction has been performed. You have to decide before you start how many significant digits will be allowed in your answer. For example, to compute 19/17 to the nearest hundredth, declare the ones column to be third from the left, with tenths and hundredths in the right two columns. Enter 19:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O O O | O O |
| | | | | | | | | | | O | | |
-----------------------------
| | | | | | | | | | O O | | |
| O O O O O O O O O | O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O | O O |
| O O O O O O O O O O O O O |
-----------------------------
```
Subtract 17 and increment the far left column as a counter:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| | | | | | | | | | | | | | |
-----------------------------
| O | | | | | | | | | O | | |
| | O O O O O O O O O O O O |
| O O O O O O O O O O | O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
-----------------------------
```
We are left with 2; you can't subtract 17 from 2 again. But, we could imagine 2 is 20 by using the tenths column. Do this, and instead of using the leftmost column as your counter, use the next one over:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| | | | | | | | | | | | | | |
-----------------------------
| O O | | | | | | | | | O | |
| | | O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O | O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
-----------------------------
```
We are left with 3 in the tenths column; you can't subtract 17 from 3, so scoot over again, and imagine the hundredths are the ones and the tenths are the tens. Subtract 17, and use the THIRD column at the left as your counter:
```-----------------------------
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
| | | | | | | | | | | | | | |
-----------------------------
| O O O | | | | | | | | O O |
| | | | O O O O O O O O | O |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O | |
| O O O O O O O O O O O O O |
| O O O O O O O O O O O O O |
-----------------------------
```
We are left with 13, and you can't subtract 17 from 13, but 13 is more than half of 17, so we can probably round up the last digit of our answer. Reading the counters on the left, we come up with an answer of 1.11, rounded up to 1.12.

The analogy to normal long division with pencil and paper should be evident.