Casting out nines

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/casting-out-nines

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical principle?Based on the properties of modular arithmetic, specifically modulo 9
2. What is the core operation?Computation of the digital root of numbers
3. How do you find a number's digital root?Add all the digits of the number together. If the sum is more than one digit, add the digits of that sum again. Keep doing this until you get a single digit, which is the digital root.
4. Why does casting out nines help check math?Because the digital root of a number is the same as the number when you look at it modulo 9. If the digital roots of the parts of a calculation match the digital root of the result, the calculation is likely correct. If they don't match, you know there is an error.

Casting Out Nines: A historical arithmetic check procedure utilizing digital roots to verify calculations.
Digital Root: The single-digit result obtained by iteratively summing the digits of a number until a single digit remains.
Modular Arithmetic: A system of arithmetic for integers where numbers 'wrap around' upon reaching a certain value (the modulus).