How does an Abacus Work?

The abacus or counting frame is an ancient calculating tool. It origins can be traced back to the Sumerian civilization about 2500 BC. It was widespread use in ancient Egypt, Greece and Persia. Today it has been largely replaced by calculators. But in Asia and Africa it is still widely used by merchants and traders.

The abacus consists of two parts, one above the other. Each part has of columns of beads. The lower part usually holds five beads and the upper part of one or two beads.

The main idea of the abacus is that tens contains ones, and the hundreds contain tens and so on. And if you have 10 ones you can just break down 1 bead in the column of tens. It means, that in lower the column we have the ones place, in the second one we have tens, in the third – hundreds, in the fourth – thousands, in fifth – tens thousands  and so on.

To calculate with an abacus you first have to input a number.  To do so, break the number down into single digits. For example break 26 into 2 ten plus 6 units. Move, from the tens column, a number of beads equal to the tens digit. In our example, this number is two. Similarly move, from the units column, a number of beads equal to the units digit. Notice that in this example that number is 6, and there are only five beads. To overcome this problem, move one bead up from the upper part of the abacus. That bead is equal to 5. Now just move 1 more beads from the lower part.

Next, input the second number. This depends on whether you are adding or subtracting. If you are adding, divide the number into digits just like above and move up further beads in addition to those already up. If you are subtracting, break down the number into digits exactly like above, but bring down beads from the ones already above.

After inputting the second number correctly you have already completed the addition or subtraction. You only need to read out the number by counting the number of beads in every column. This will give you the value of each digit. Of course if the value of any digit exceeds nine, subtract 10 from the value and add 1 to the digit at one larger place value. For example, if you get 2 in the hundreds position, 13 in the tens position, and 1 in the units position, subtract 10 from the 12 in the tens position and add 1 to the 2 in the hundreds position. This will give you a result of 331.

Still confused? Check out this video to learn how to multiply and substract with an abacus.

If you need in-person help to learn how an abacus works in particular or the math related to it we recommend to find an abacus-math tutor.