Digital Roots

8/12/2019 Digital Roots

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Digital Root A simple and useful mathematical concept

Santha Fernandez 2013 Page 1

Introduction

The digital root (DR) concept is the idea that any number greater than 9 can be reduced to a singledigit by adding the component digits of the number in one or more steps.

How to find the DR

Simply, add the individual digits of the number in one or more steps until you obtain a single digit(1, 2, 3 or 9 ) and that is the digital root of that number. For example:

i. 42 4+2 = 6ii. 84 8+4 = 12 1+2=3

iii. 737 7+3+7 = 17 1+7=8iv. 6789 6+7+8+9 = 30 3+0 = 3

Shortcuts to finding the DR1. The digital root of any number containing only 9s (such as 99 or 999 or 9999) is 9.2. If there is one or more 9s in a number simply ignore them and add the remaining digits.3. Look for digits that you can quickly add to 9, or to multiples of 9; ignore them and add the

remaining digits. For example:

i. 19 19 1ii. 998 998 8

iii. 3198 3198 3iv. 6566 6566 5v. 7781 7781 7+7=14 1+4 5

Use the DR concept in school work

Mastering the DR concept can help you improve your numeracy skills and to achieve better gradesat school. This is because the DR concept can be used to check that your answers to your arithmeticproblems are correct.

Basically, in any addition, subtraction or multiplication problems the final DR on either side of anequation must be the same. The DR can also be used to double check your division problemsalthough the steps are slightly different.

Here, I will demonstrate how you can use the DR to check that your answers to arithmetic problemsare correct.


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Addition (A + B = C)

Addition A + B = CIs the answer

correct ( or )?Why or why not?

Example 1 27 + 32 = 59

Work out DR of numbers on eitherside of equation 9 5 5

Add and find the final DR on leftside of equation; check if it equals DRon right side of equation

9 + 5 5 5

DR of 5 on both

sides of theequation

Example 2 47 + 26 = 74



2 + 8 = 10 1 2

DR of 1 on one sideand 2 on other side

of the equation

Example 3: Try this 47 + 26 = 73

Work out DR of numbers on eitherside of equation



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Subtraction (A B = C)

Note: In subtracting the DR of B from the DR of A it is possible that we may end up with 0 or anegative value. If we do get such a value we need to find the complement digital root value all weneed to do is add 9 to it.

Subtraction A - B = CIs the answer


Example 1 99 - 26 = 73


Subtract and find the final DR onleft side of equation; if it is not 0 or anegative number check if it equals

DR on right side of equation.

9 8 = 1 1

DR of 1 on both sidesof the equation

Example 2 133 - 52 = 81


7 7 9

Subtract and find the final DR onleft side of equation; if it is not 0 or anegative number check if it equalsDR on right side of equation.

7-7= 0; since it is 0we find its

complement byadding 9, i.e. 0 + 9 =

9

9


Example 3 74 - 26 = 48



2 8 = -6; since it isa negative value wefind its complementby adding 9 i.e. -6 +

9 = 3

3


Example 4 567 - 444 = 223



9 - 3 = 6 7

DR of 6 on one sideand 7 on other side of

equation

Example 5: Try this 567 - 444 = 123




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Multiplication (A x B = C)

Multiplication A X B = CIs the answer


Example 1 15 x 14 = 210

Work out DR of numbers oneither side of equation 6 5 3

Multiply and find the final DR onleft side of equation; check if it equalsDR on right side of equation.

6 x 5 = 30 3 3DR of 3 on both

sides of theequation

Example 2 24 x 36 = 863

Work out DR of numbers oneither side of equation 6 9


6 x 9 = 54 9 8DR of 9 on oneside and 8 onother side of

equation

Example 3: Try this 14 x 37 = 618

Work out DR of numbers oneither side of equation



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Note:

You can also use the DR concept to check more complex arithmetic problems. Just remember tofollow the mathematical BODMAS rule, i.e. solve brackets, orders (i.e. powers, square roots etc.),division, multiplication, addition and subtraction

Example 1

20 x 3 +14 = 74DR on right side is 2DR on left side of equation is 2 x 3 + 5 6 + 5 11 2Your answer is correct

Example 2

(4+3) 2 + 7 2x6= 44

DR on right side is 8DR on left side of equation is 7 x 7 + 7 12 49 + 7-3 11 3 8Your answer is correct

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