Digital Roots to Check Answers to Addition Questions

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This next exercise is only for those students with a mastery of digital roots and the ability to follow multiple instructions through a somewhat complicated algorithm. This may need parental supervision. I tried this with grades 2-5. If your child has trouble with this, have them only focus on the digital root practice in the previous post.

One way of quickly checking whether a sum involving large numbers is correct is to take the digital roots of the numbers, add them, reduce the answer to a digital root, and then see if it corresponds to the digital root of the answer. If they don't match, the answer is wrong. If they do match, the probability is fairly high that the answer is correct.

 Example:              Suppose we are adding two numbers: 345 + 789.

· The Digital Root of 789 is 6.

· The Digital Root of 345 is 3

· Now add the two digital roots: 3 + 6 = 9

· This implies that the Digital Root of our final answer

obtained after adding 345 + 789 will be 9.

· Let’s verify that 345 + 789 = 1134

· The Digital Root of 1134 = 1 + 1 + 3 + 4 = 9 This equals the sum

obtained at by adding the digital roots of the original two

numbers above.

List Numbers Vertically                                        Calculate the Digital Root

And Find the Sum                                                    of each Number and add       

                                                                                    Those Digital Roots*     

        789           7+8+9=24; 2+4=          6

 +345            3+4+5=12; 1+2=       +3

1,134         1+1+3+4=                       9         

Let's try another example.

List Numbers Vertically                                        Calculate the Digital Root

And Find the Sum                                                    of each Number and add       

                                                                                    Those Digital Roots*     

123456789 9

234567891 9

 +987654321 + 9

_____________ ______

  1345679001     1+3+4+5+6+7+9+0+0+1=2+7= 9

Use the document from the previous post entitled Digital Roots 2-7 Digits to choose numbers to add here. See the pdf entitled Digital Roots Addition to practice this beautiful algorithm developed by Gauss in 1800.

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