Calculators have only recently gained widespread popularity for their help in solving arithmetic problems which might be too difficult to figure out mentally. Even paper, pens and pencils are a luxury that we have only been able to enjoy relatively recently in the wider scope of history.
Abacuses, however, have been around for hundreds of years. They are very simple devices which can be used to solve relatively complex math problems. Even today in Japan, the abacus is still very popular and is taught in schools. The best abacus users can usually perform calculations faster than a calculator, although this takes a lot of practice.
An abacus is actually quite easy to use, once you understand the basics. If you look at an abacus, you will see a series of vertical columns. Each of those columns represents a base 10 unit. So the right-most column represents the ones-unit, the second-from-left column represents the tens-unit, the third column represent the hundreds-unit, and so forth. The more vertical columns that are on the abacus, the larger the number you can work with.
Each vertical column is broken up into two sections. There is an upper section and a lower section (the ancient Chinese called them the heavenly section and the earthly section). The upper section contains only one bead, and it can be in one of two positions: up or down. The lower section contains 4 beads, and they can also be either up or down.
The lower beads each represent 1 unit, while the upper bead represents 5 units. For a bead to be “active”, it must be in the position towards the center of the device. So this means “down” for the top section and “up” for the lower section.
Let’s look at an example:
Say that I want to represent the number “18” on an abacus. It’s just like you were taught in elementary school. You need to put a “1” in the tens-unit column and an “8” in the ones-unit column. To represent a “1” in the tens-unit column, you would simply slide one of the beads in the lower section toward the center. To represent an “8” in the ones-unit column, you need to slide the upper bead toward the middle (5), and three of the lower beads toward the middle. An active upper bead and 3 active lower beads represents an “8”.
Can you picture our imaginary abacus? Now let’s try a simple math problem. Let’s subtract 6 from 18.
18 – 6 = ?
Our abacus is already showing 18, so all we need to do is subtract 6 and we should get our answer. In the ones-unit column, slide the upper bead away from the center and slide one of the lower beads away from the center. Now we should have one active bead in the tens-unit column and 2 active beads in the ones-unit column. That represents “12”, so we know that:
18 – 6 = 12
That was a simple example, but hopefully you can see how you might be able to perform many more complex math problems on an abacus. So if you haven’t tried using an abacus yet…why not? Maybe you don’t need that fancy calculator after all!