# Mental Math: Digital Root Extraction

5 Steps
Continuing in the tradition of my first 2 Instructables, I present to the interested reader a new mental math technique today. This trick, like the first 2 tricks, is for most intents and purposes simply a parlor trick to astound and amaze your fellow geeks at your next math club meeting. That said, there is an obscure set of circumstances where it could have some practical value.

So, without further ado, I present to you digital root extraction.
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## Step 1: What is a Digital Root?

"What is the digital root?", you ask. The digital root is an obscure mathematical operation in which a user recursively adds together all of the digits of a number until only a single remains. This remaining number is known as the digital root.

A better demonstration would be to take a number (such as 179) and demonstrate. So, the digital root of 179 is something like this:

179 -> 1+7+9 = 17 -> 1+7 = 8

So, the digital root of 179 is 8.

Another, more interesting way to look at a digital root is that it is a modulo 9 operator. In other words, if you were to divide the number by 9, the integer remainder and the digital root are the same thing. So, digital roots can be rewritten as mod9(Number).

Now that we know what digital roots are, let's go ahead and find them.
mluft says: Aug 29, 2009. 6:19 AM
so, i am a 4th grade teacher and i'm teaching my students about digital root. i'm teaching them that it is a tool to use to check computation. i have a parent all up in my face saying it is too abstract for 4th graders and it is some new-fangled crap i'm teaching that is going to screw up her kid's understanding of math for life. i've searched and searched for something, anything to help her understand, but no luck. any ideas?
purduecer (author) in reply to mluftSep 2, 2009. 5:29 AM
In case you didn't know already, you can find out more about the digital root here. Digital roots are a topic that is indeed fairly abstract in math, but as you mentioned, they can be a quick but useful way to check hand computations. If I were you, and trying to explain to the parent, I would mention simply that you're teaching your kids a helpful shortcut for finding the remainder, and remind the parent that when they add all the digits together to see if a number is divisible by 9, they are in fact already taking the digital root.

Hope that helps, let me know.
foobear says: Oct 27, 2008. 10:43 AM
Thank you, this is wonderful. I always wondered what the term "casting out 9s" meant. Please show us how to do the division one too.

Perhaps you could team up with this guy: math museum and maybe this guy:
advanced subject explained with ascii art

And one day they could make the perfect math book that would actually imbue the average math phobe with a true intuition for math! A sort of "math pill" if you will.
purduecer (author) in reply to foobearOct 27, 2008. 1:42 PM
haha, thanks for the praise (nice secret squirrel icon, btw). I will continue to post math instructables as I discover them, and in the meantime will try and bring interesting material to the Instructables fan. --Purduecer