You can also assign some columns to be decimal places if necessary. For example, if you are representing a number like 10. 5, then the furthest right column would be the tenths place (the first decimal place), the second column would be the ones place, and the third column the tens place. Likewise, to represent a number like 10. 25, the furthest right column would be the hundredths place, the second column would be the tenths place, the third the ones place, and the fourth the tens place.
You’ll find it easiest to use your thumb to move the beads in the bottom row, and your index finger to move the beads in the top row.
For example, 11 would have one bead in the second column pushed up, and another in the first column pushed up, all on the bottom row. Twelve would have one in the second column and two in the first column, all pushed up, and all on the bottom row. Two hundred and twenty six would have two in the third column pushed up in the bottom row, and two in the second column pushed up in the bottom row. In the first column, one bead on the bottom row would be pushed up, and the bead on the top row would be pushed down.
In the ones column, you’ll do essentially the same thing. Eight plus 4 equals 12, so you’ll carry the one over to the tens place, making it 1. This leaves you with 2 in the ones place.
Eight from nine is one, so you’ll leave a single bead up in the hundreds place. In the tens place, you can’t subtract 6 from 3, so you’ll borrow the 1 in the hundreds place (leaving it zero) and subtract 6 from 13, making it 7 in the tens place (the upper bead up and two lower beads). Do the same thing in the ones place, “borrowing” a bead from the tens place (making it 6) to subtract 7 from 12 instead of 2. There should be a 5 in the ones column: 932 - 867 = 65.
The “X” and “=” will be represented by blank columns. The abacus should have 3 beads up in the farthest column left, four up in the next farthest, a blank column, a column with one bead up, two beads up in the next, and another blank column. The rest of the columns are open.
If you are multiplying larger numbers, keep the same pattern: start with the leftmost digits, and work to the right.
First, multiply 3 and 1, recording their product in the first answer column. Push three beads up in that seventh column. Next, multiply the 3 and the 2, recording their product in the eighth column. Push one bead from the upper section down, and one bead from the lower section up. When you multiply the 4 and the 1, add that product (4) to the eighth column, the second of the answer columns. Since you’re adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column (four beads from the bottom section pushed up to center bar) and a 0 in the eighth (all beads in their original starting position: the top section bead pushed up, bottom section beads pushed down). Record the product of the last two digits 4 and 2 (8), in the last of the answer columns. They should now read 4, blank, and 8, making your answer 408.
For example, to divide 34 by 2, count 2 in the left-most column, leave two blank columns, then put 34 over to the right. Leave the other columns blank for the answer section. To do this, push two lower beads from the bottom portion up in the left-most column. Leave the next two columns alone. In the fourth column, push three beads from the bottom portion up. In the fifth column from the left, push four beads from the bottom portion up. The blank columns between the divisor and the dividend are just to visually separate the numbers so you don’t lose track of what’s what.
To do this, push one bead from the bottom portion up in the first column of the answer section. If you like, you can skip a column (leave it blank) between the dividend and the columns you want to use for the answer section. This can help you distinguish between the dividend and the work you do as you calculate.
To make the dividend read 14, push two of the bottom portion beads currently pushed up to the center bar at the fifth column back down to their starting position. Only one bead in the lower portion of the fifth column should remain pushed up to the center bar.
Two beads from the bottom portion of the left most column will be pushed up to the center bar. This will be followed by several blank columns. One bead from the bottom portion of the first answer section column will be pushed to the center bar. In the next answer section column, two beads from the bottom portion will be pushed up to the center bar, and the bead from the top portion will be pushed down to it.
