Arithmetic of Digital Root

By Kardi Teknomo, PhD.

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In the previous section, we have learned the pattern of digital roots. In this section, we will explore the properties of simple arithmetic of digital roots.

Suppose we have two digital roots, and , then we would like to know

Here is the addition table of digital roots and its pattern.

Addition

Below is the Subtraction table of digital roots and its pattern

Subtraction

You will see number 9 in the main diagonal and the other digital roots lie in parallel with the diagonal.

Multiplication

Multiplication table produces many beautiful pattern and properties that worth to put into separate section to describe about it. More about multiplication table, see Vedic Square

Division

Digital root 3, 6 and 9 are special. Not all numbers can be divided by these three numbers. If the division is allowed, it will produce multiple roots.

Notice that 3, 6 and 9 has no root or multiple roots. For example, 1/3 has no root (undefined, similar to a number divided by zero in decimal system) but 6/3 has multiple roots of 2, 5 and 8. Digital root 9 has no root unless the denominator is also 9 which produce 9 multiple roots of 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Factors

Suppose , and are digital roots and we have equation then we have solution ,

1. no solution (no root) if and
2. multiple solutions (multiple roots) if and
3. Single solution (single root) if otherwise

Digital Root Identity

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Download the MS Excel companion of this tutorial here

The PDF file of this tutorial is also available for download here.

This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. Digital Root. http:\\people.revoledu.com\kardi\ tutorial\