How to Multiply on an Abacus?

Since multiplication is repeated addition, any multiplication problem can be solved on an abacus. To perform multiplication on an abacus, students must be able to perform addition on the abacus and memorize the basic single digit multiplication facts through 9×9. With addition and the basic math facts, students can take on any multiplication problem with ease. If you are not familiar with abacus addition please take a look at our beginning abacus lessons. There are several tools for memorizing your multiplication facts on in the Facts Training and Tools Modules.

This post will describe the basic approach to multiplication on the abacus. If you are ready to jump straight into some examples please see Multiplication with a Single Digit Multiplier and Multiplication with a Double Digit Multiplier.

Abacus users first set up their multiplication problem on the abacus by choosing a reference rod, the unit rod, and a starting rod. The starting rod is found by counting the total number of digits in both the multiplicand and multiplier then counting this number of rods left of the unit rod. 

From the starting rod, users process each digit of the multiplier with each digit of the multiplicand moving one rod right as they move through the digits. For each single digit multiplication, the user enters a two digit answer to ensure proper place value alignment as they work through problem. For example, if we had the math fact 5×1=5, the student would enter two digits 05 on the abacus instead of just a single digit 5. At the end of the calculation the user will arrive at the chosen reference rod with the complete answer.

Students that learn multiplication on the abacus develop both speed and accuracy because of the simple, efficient mechanization of the multiplication process.