Ask Dr. Math Casting Out Nines

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 Casting Out Nines, a selection of answers from the Dr. Math archives. Divisibility Rules - Dr. Math FAQ How can you tell whether a number is divisible by another number (leaving no remainder) without actually doing the division? Why do "divisibility rules" work? From the archives: Casting Out Nines to Check Arithmetic Can you explain how to use the 'casting out 9's' technique in a way that a 6th grader can understand? Casting Out Nines I am trying to find a reference that defines this mathematical operation... Casting Out Nines and Elevens Why is nine used in proving this math answer? When Casting Out Nines Fails To prove that casting out 9's worked, I intentionally used an incorrect quotient, but was shocked when the problem checked out correctly. Casting Out Nines - Proof Show that if the order of the digits of a natural number is permutated to form a new number, the difference between the old number and the new number is divisible by 9. Accountants Use 9 to Check for Errors I know accountants divide the difference of debits and credits by 9 to check for a transposition error. I need to understand why this works. Even or Odd in Base 5? Is there a way to find whether a number written in base 5 is even or odd without first converting it to base ten? Sum of the Digits of Multiples of 9 Why do the digits of nine times a single-digit number add up to 9?