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Abacus Division

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When setting up problems of division on the abacus, the dividend is set on the right and the divisor is set on the left. The abacus committee suggests leaving 4 unused rods between these two numbers. It is on these unused rods where the quotient answer is formed.

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Dividing one number in the divisor into one or possibly two numbers of the dividend at a time does division. The operator multiplies after each division step and subtracts the product. The next part of the dividend is then tracked onto the remainder and the process continues. It is much like doing it with a pencil and a paper.


1: where the digits in a divisor are less than (or equal to) the corresponding digits of the dividend, begin by replacing the quotient two rods to the left of the dividend.

2: where the digits in the divisor are greater than the corresponding digits of the dividend, begin by placing the first number in the quotient next to the dividend.


951 / 3 = 317

In this example the dividend has 3 whole numbers. Chose the unit rod and count 3 rods to the left. The divisor has one whole number so count one plus two back to the right.

Step 1

Set the dividend 951 and the divisor 3 on rods on the abacus.

Step 2

The divisor 3 is smaller than the first letter of the dividend i.e. 9. Therefore apply rule 1 and set the first number in the quotient two rods on the left. Divide 3 with 9 and set the quotient 3 on the rod.Multiply the quotient 3 by 3 and subtract the product 9 from the other rod. This leaves the partial quotient 3 and the remainder of the dividend 51 on rods.

Step 3

Divide into 5. Once again the divisor is smaller than the dividend so follow rule 1. Set the quotient 1 on the rod.Multiply the quotient 1 by 3 and subtract the product 3 from 5. This leaves the partial quotient 31 and the remainder of the dividend 21 on the rods.

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Step 4

Divide 3 into 21 and set the quotient 7 on the rods.Multiply the quotient 7 by 3 and set subtract the product 21 from rods leaving the answer 317 on the rods.

Thus the division is done on the abacus more conveniently.

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Dear team,
Pl. help me out in solving division which involve multiple of fractions or double/multiple digit division

Comment posted by: sonika malhotra on 2010-02-23T03:51:57
do you have a formula for multiplication on the abacus please? thanks
Comment posted by: kovi on 2010-03-29T06:09:14
Dear team
please send me formulas of division with abacus system.
Comment posted by: Satvir Chand on 2011-04-05T11:55:09

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