How to do Division with a Single Digit Divisor on the Abacus?

If this is your first time doing division on the abacus please see a more basic example, How to Divide on the Abacus. In this example, we will show how to do basic division with a single digit divisor on the abacus which can be thought of as long division. Division is usually difficult for most students to learn. Again this is where the abacus will shine giving students a straight forward, simple approach to solving division problems. Just like in the standard division algorithm, we will transform division problems into a series of subtraction facts as we move the divisor through the dividend. In the following examples we will know we have completed the division problem when the subtraction process has reduced the dividend to zero. In more advanced division problems, the program will show students how to handle decimal division where the answers will need to rounded to a specific number of significant digits. For now let’s work out some basic abacus division examples.

We will transform division into a series of subtraction facts again using our knowledge of the 9×9 multiplication facts we memorized for multiplication. In this problem example we will continue the division process until there is no dividend remainder left, i.e. zero, to find the quotient answer.

 Let’s consider the following example.

First we need to setup our division problem on the abacus. We will show the divisor for clarity but typically we would not take the time to place the divisor on the abacus. You will notice that we chose a quotient unit rod that coincides with the first digit of the dividend. Choosing this quotient unit rod is not a problem since after the first subtraction we will remove the first dividend digit. If we can, by convention we place the quotient on 4 rods between the divisor and dividend. For larger quotient answers we will not place the divisor on the abacus to provide more calculating space.

To begin our abacus math division we compare the divisor 6 with the first dividend digit 5. Since 6 is larger than 5 we will compare the divisor 6 with the first two dividend digits 51. Since we moved 1 rod to the right on the dividend will also move 1 rod right on the quotient to the 3rd quotient rod. Because 6×8 = 48 (and 6×9 = 54 which is larger than 51) we will place 8 as the first quotient digit on the 3rd rod and subtracting 48 from 51 on the dividend leaving 342 on the dividend.


Moving one more rod to the right on the dividend we compare the divisor 6 to 34 on the dividend. Since 6×5 = 30 we place 5 as the second quotient digit and subtract 30 from 34 on the dividend leaving 42 remaining on the dividend.

Again moving one more rod right on the dividend we compare the divisor 6 with 42 remaining on the dividend. Since 6×7 = 42, we place 7 as the 3rd quotient digit on the quotient unit rod and subtract 42 from 42 on the dividend. Since we have zeroed out the dividend our final answer is 857.