100 LearnersLast updated on May 26th, 2025
Divisibility Rule of 9
The divisibility rule is a way to determine whether a number is divisible by another number without performing actual division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 9.
What is the Divisibility Rule of 9?
The divisibility rule for 9 is a method by which we can find out if a number is divisible by 9 without using the division method. Check whether 234 is divisible by 9 with the divisibility rule.
Step 1: Add all the digits of the number together. For 234, add 2, 3, and 4. 2 + 3 + 4 = 9.
Step 2: Check if the result from Step 1 is a multiple of 9. Since 9 is a multiple of 9, the number 234 is divisible by 9. If the sum isn't a multiple of 9, then the number isn't divisible by 9.
Tips and Tricks for Divisibility Rule of 9
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 9.
Know the multiples of 9:
Memorize the multiples of 9 (9, 18, 27, 36, 45, etc.) to quickly check divisibility. If the sum of the digits is a multiple of 9, then the number is divisible by 9.
Use the sum of digits:
Even if the sum of the digits is a large number, you can sum those digits again. For example, if the sum is 18, then add 1 and 8 to get 9, which is a multiple of 9.
Repeat for large numbers:
For larger numbers, keep summing the digits until you reach a small number. For example, check if 1983 is divisible by 9.
Add the digits: 1 + 9 + 8 + 3 = 21
Since 21 is not a multiple of 9, add again: 2 + 1 = 3.
Since 3 is not a multiple of 9, 1983 is not divisible by 9.
Use the division method to verify:
Students can use the division method to verify and cross-check their results. This helps to confirm and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 9
The divisibility rule of 9 helps us quickly check if a given number is divisible by 9, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes to help avoid them.
Mistake 1
Not summing all digits.
Ensure all digits are added together accurately to check if the sum is a multiple of 9.
Divisibility Rule of 9 Examples
Problem 1
Can a store manager determine if a sum of $162 is divisible by 9?
Yes, $162 is divisible by 9.
Explanation
To check if 162 is divisible by 9, add the digits together: 1 + 6 + 2 = 9. Since 9 is a multiple of 9, the original number, 162, is also divisible by 9.
Problem 2
A teacher has 243 pencils and wants to divide them evenly among 9 students. Is this possible using the divisibility rule of 9?
Yes, 243 can be evenly divided among 9 students.
Explanation
To determine if 243 is divisible by 9, add the digits: 2 + 4 + 3 = 9. Since 9 is a multiple of 9, 243 is divisible by 9.
Problem 3
A student calculates that the sum of her test scores is 567. Can she check if this total is divisible by 9?
Yes, 567 is divisible by 9.
Explanation
Add the digits of 567: 5 + 6 + 7 = 18. Then, add the digits of the result: 1 + 8 = 9. Since 9 is divisible by 9, 567 is also divisible by 9.
Problem 4
A baker has 444 cookies and needs to pack them equally into boxes of 9. Can he do this using the divisibility rule of 9?
No, 444 is not divisible by 9.
Explanation
Add the digits of 444: 4 + 4 + 4 = 12. Since 12 is not a multiple of 9, 444 is not divisible by 9.
Problem 5
An artist is arranging 729 tiles into a pattern with 9 equal rows. Is this configuration possible based on the divisibility rule of 9?
Yes, 729 is divisible by 9.
Explanation
To check if 729 is divisible by 9, add the digits: 7 + 2 + 9 = 18. Then, add the digits of the result: 1 + 8 = 9. Since 9 is a multiple of 9, 729 is divisible by 9.
FAQs on Divisibility Rule of 9
1.What is the divisibility rule for 9?
2.How many numbers are there between 1 and 100 that are divisible by 9?
3.Is 54 divisible by 9?
4.What if I get 0 after summing the digits?
5.Does the divisibility rule of 9 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 9?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 9 with numbers?
8.What role do numbers and Divisibility Rule of 9 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 9 skills?
Important Glossaries for Divisibility Rule of 9
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number. For example, a number is divisible by 9 if the sum of its digits is a multiple of 9.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 9 are 9, 18, 27, 36, etc.
- Integers: Integers include all whole numbers, negative numbers, and zero.
- Summation: The process of adding numbers together to find their total.
- Verification: The process of confirming results, often by using another method, such as actual division.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
