The "nine rule" in math commonly refers to the divisibility rule of 9.
Divisibility Rule of 9 Explained
The divisibility rule of 9 is a simple way to determine if a number is divisible by 9 without performing long division. According to this rule, if the sum of all the digits of a number is divisible by 9, then the number is divisible by 9.
How to Apply the Divisibility Rule of 9
Here's how to apply the divisibility rule of 9:
- Add up all the digits in the number you want to test.
- Check if the sum is divisible by 9.
- If the sum is divisible by 9, the original number is also divisible by 9.
Examples of the Divisibility Rule of 9
Let's look at some examples:
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Example 1: Is 81 divisible by 9?
- Sum of digits: 8 + 1 = 9
- 9 is divisible by 9.
- Therefore, 81 is divisible by 9.
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Example 2: Is 126 divisible by 9?
- Sum of digits: 1 + 2 + 6 = 9
- 9 is divisible by 9.
- Therefore, 126 is divisible by 9.
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Example 3: Is 954 divisible by 9?
- Sum of digits: 9 + 5 + 4 = 18
- 18 is divisible by 9.
- Therefore, 954 is divisible by 9.
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Example 4: Is 235 divisible by 9?
- Sum of digits: 2 + 3 + 5 = 10
- 10 is not divisible by 9.
- Therefore, 235 is not divisible by 9.
Table Summary of Divisibility Rule of 9
| Number | Sum of Digits | Divisible by 9? | Result |
|---|---|---|---|
| 81 | 9 | Yes | Divisible |
| 126 | 9 | Yes | Divisible |
| 954 | 18 | Yes | Divisible |
| 235 | 10 | No | Not Divisible |
Practical Insights
- The divisibility rule of 9 is helpful for simplifying fractions and checking calculations.
- It provides a quick way to determine if a number is a multiple of 9.
