How Do You Determine if a Number is Divisible by 9?
A number is divisible by 9 if the sum of its digits is divisible by 9.
The divisibility rule for 9 is a simple yet powerful tool for determining if a number is divisible by 9 without performing the actual division. This rule states:
- Add all the digits of the number together.
- If the sum is divisible by 9, then the original number is also divisible by 9.
This rule works because of the properties of modular arithmetic. Essentially, any number is congruent to the sum of its digits modulo 9.
Examples
Let's illustrate this with a few examples:
- Example 1: Is 18 divisible by 9? 1 + 8 = 9. Since 9 is divisible by 9, 18 is divisible by 9.
- Example 2: Is 549 divisible by 9? 5 + 4 + 9 = 18. Since 18 is divisible by 9 (18/9 = 2), 549 is divisible by 9.
- Example 3: Is 247 divisible by 9? 2 + 4 + 7 = 13. Since 13 is not divisible by 9, 247 is not divisible by 9.
Practical Application and Insights
This rule is particularly useful for:
- Mental math: Quickly checking divisibility without a calculator.
- Error detection: Verifying calculations, especially when dealing with large numbers.
- Problem-solving: Solving divisibility problems in algebra and number theory.
Multiple sources (Cuemath, Byju's, Mathnasium, Smartick, Grayson College, Reddit, Maths with Mum, Reddit, Math Stack Exchange, Chegg) confirm the accuracy and efficiency of this method. The YouTube video further demonstrates its practical application.
