In the text below you can read information about the divisibility rule of 9. In addition to the rule, on the page, you can see many examples that describe in detail how to use the rule for determining the divisibility of the number 9. This rule and this method can help you examine whether a certain number is divisible by the number 9 or not. The rule and the procedure itself for determining divisibility by this number are very simple, but we still recommend that you pay attention to it to memorize it permanently. You will be able to use divisibility by the number 9 later to solve certain more complicated math problems more easily!
Divisibility Rule For 9
The divisibility rule of 9 is: A number is divisible by 9, if and only if, the sum of its digits is divisible by 9!
If the condition mentioned in the rule itself is met, then we can be sure that that number is divisible by the number 9!
Let’s look at some examples of determining the divisibility rule of 9! Take a close look at the examples on the page below:
Examples Using The Divisibility Rule Of 9
Example 1: Determine if the number 135 is divisible by the number 9!
To use the divisibility rule of 9, which we have already defined above in this text, we need to calculate the sum of the digits of the number 135! Let’s do it!
1+3+5=9
The sum of the digits of the number 135 is 9. Because the sum of 9 is divisible by the number 9, it follows that the number 135 is divisible by the number 9! If we want to check the accuracy of the claim and the result we can check with the help of a calculator. We will establish that:
135:9=15
When dividing 135 by 9, the result is 15 (a whole number), without a remainder, which means that the number 135 is indeed divisible by the number 9!
Example 2: Determine if the number 563 is divisible by the number 9!
The sum of the digits of the number 563 is:
5+6+3=14
The sum of the digits of the number 563 is 14. Because the sum is not divisible by 9, it follows that the number 563 is not divisible by 9! If we check with a calculator we get the following result:
563:9=62,(5)
The fact that dividing 563 by the number 9 yields a result that is a decimal number confirms that the number 563 is indeed not divisible by 9!
By Bigger Number
Example 3: Determine if the number 12735 is divisible by the number 9!
The sum of the digits of the number 12735 is:
1+2+7+3+5=18
The sum of the digits of the number 12735 is 18. Because the sum of 18 is divisible by 9, it follows that the number 12735 is divisible by 9! If we check with a calculator, the following expression is obtained:
12735:9=1415
When dividing 12735 by 9, the result is 1415 (a whole number), without a remainder, which means that the number 12735 is indeed divisible by the number 9!
Conclusion
As can be easily seen from the solved examples in the text above, in which the divisibility rule of 9 is practically used, the whole procedure is extremely easy to use. We can make the calculation very simple if the number we are considering is two-digit, three-digit, or four-digit. If the number has more digits, then the testing itself is again easy, but it will take us more time than with numbers with fewer digits!
In the video below you can see many more examples of determining divisibility by 9 in video format, presented in a much more interesting way! Check out the video examples too!
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