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Rule of the Sum of the Digits: This is a mathematical rule that helps us find out if a number is divisible by 3 or 9. To use this rule, we add up all the digits in the number. If the sum is divisible by 3, then the original number is also divisible by 3. If the sum is divisible by 9, then the original number is also divisible by 9. For example, if we have the number 123, we add 1+2+3=6. Since 6 is divisible by 3, we know that 123 is also divisible by 3.
Definition: The rule of the sum of the digits is a mathematical principle that states that the sum of the digits of a number can provide information about the number itself.
For example, if we take the number 123, the sum of its digits is 1+2+3=6. This means that any number that is divisible by 3 must also have a sum of digits that is divisible by 3. In this case, 123 is not divisible by 3, but 132 is, because 1+3+2=6, which is divisible by 3.
Another example is the number 456. The sum of its digits is 4+5+6=15. This means that any number that is divisible by 9 must also have a sum of digits that is divisible by 9. In this case, 459 is divisible by 9, because 4+5+9=18, which is divisible by 9.
The rule of the sum of the digits is a useful tool in mathematics, especially in number theory and algebra. It can help to quickly determine whether a number is divisible by a certain factor, and can also be used to find patterns in numbers.