The abacus as shown in the figure is divided lengthwise into two unequal parts by an horizontal beam or bar.
The number of beads in each column is seven; two above the beam and five below it. For convenience the beads above the beam are called altobeads, and those below it, hypobeads.
One altobead is equivalent to five hypoheads.
The value of a bead depends upon which column is assumed to be the units' column, normally the right-hand one.
The beads in the left-hand column are greater than those in the right-hand column. One unit in the left column is always ten times as large as one unit in the adjacent column on the right.
Thus, if we assume that the first column on the right-hand side of the frame to be the units' place, one hypobead in the first column will be worth one unit; one in the second column will be worth ten units; one in the third column will equal to une hundred units, etc.
Likewise, one altobead in the second column will equal 50 units, and so on.
Before using the abacus all the altobeads should be placed against the upper side of the frame and all of the hypobeads against the lower side. This is the neutral position.
Done this, they are ready to be moved up or down the frame for recording any number. The middle beam is where the computation is arranged.
Instead of moving the last hypobead to make 5, an altobead may be used and the four hypobeads returned to neutral position.
Similarly, since one hypobead in the left column is equal to two adjacent right-hand altobeads, instead of using the upper altobeads to make 10, one hypobead on the left column may be used and the lower altobead returned to neutral.
It is always advisable, especially for a beginner to check the results of a computation. For this purpose one of two methods may be adopted:
Addition and subtraction and also multiplication and division may be conducted to verify each of its opposite process. Thus, an example on addition may be checked by subtraction and vice-versa; and the same is true with multiplication and division.
But the general method used by the abacists is to repeat the work.
In this web page you can practice with the abacus clicking on the exercises' link, where you will also check your results by clicking on the red arrow.
Click in this link to practice your skills.
