Last updated on May 26th, 2025
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.
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.
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule 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.
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.
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.
Students can use the division method to verify and cross-check their results. This helps to confirm and also learn.
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.
Can a store manager determine if a sum of $162 is divisible by 9?
Yes, $162 is divisible by 9.
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.
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.
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.
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.
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.
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.
Add the digits of 444: 4 + 4 + 4 = 12. Since 12 is not a multiple of 9, 444 is not divisible by 9.
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.
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.
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.
: She loves to read number jokes and games.