By Robert Preston • Updated Aug 30 2022
The abacus is a time‑tested computational tool that has powered arithmetic from ancient China to modern classrooms. Its design—rows of beads separated by a horizontal bar—allows users to perform addition, subtraction, and more complex operations with speed and precision.
Slide every bead to the far edge of its column, ensuring none touch the central bar.
Each column represents a single decimal digit. The right‑most column is ones, the next left is tens, and so on.
Move the bottom beads upward to the bar: one bead for 1, two for 2, up to four for 4.
Slide all four bottom beads down, then bring one top bead to the bar. The bottom beads stay at the bottom.
Keep the five bead at the bar and move 1‑4 bottom beads upward to add the remaining value.
When a column reaches 10, slide all beads away from the bar, then move one bead from the adjacent left column onto the bar to carry the extra value.
Arrange the beads to display the initial value you wish to modify.
For addition, move the required number of bottom beads up in the right‑most column. For subtraction, move beads down, then shift the top bead away and bring the remaining bottom beads back to the bar.
When a column exceeds 9, clear its beads, then place a bead on the next left column to represent the carry‑over.
If you need to subtract a larger digit from a smaller one, take a bead from the next left column, move all beads in the current column to the bar, and continue subtracting.
Continue the above steps for each column, moving leftward until the most significant digit is processed.
To use a hexagonal abacus for decimal work, simply ignore the top bead of the upper row and the bottom bead of the lower row in each column.
