What is Divisibility by 9?

S1-SA1-0166

Grade Level:

Class 4

Maths, Computing, AI

Definition

What is it?

Divisibility by 9 means a number can be divided by 9 without leaving any remainder. It's like sharing a total equally among 9 friends, where everyone gets the same whole number of items.

Simple Example

Quick Example

Imagine you have 45 ladoos. If you want to share them equally among 9 people, can you do it without any ladoos left over? Yes, because 45 divided by 9 is 5. So, 45 is divisible by 9.

Worked Example

Step-by-Step

Let's check if 738 is divisible by 9.

Step 1: Add all the digits of the number. For 738, the digits are 7, 3, and 8.
---Step 2: Sum the digits: 7 + 3 + 8 = 18.
---Step 3: Now, check if this sum (18) is divisible by 9. We know that 18 divided by 9 is 2.
---Step 4: Since the sum of the digits (18) is divisible by 9, the original number (738) is also divisible by 9.

Answer: Yes, 738 is divisible by 9.

Why It Matters

Understanding divisibility rules helps you quickly check numbers without a calculator, which is useful in computing for error checking and in AI for optimizing calculations. Engineers and data analysts use these quick checks for large datasets to ensure accuracy and efficiency.

Common Mistakes

MISTAKE: Checking if the last digit is even or odd. | CORRECTION: Divisibility by 9 depends on the SUM of the digits, not just the last digit.

MISTAKE: Confusing divisibility by 9 with divisibility by 3. | CORRECTION: While a number divisible by 9 is always divisible by 3, the reverse isn't true. The sum of digits must be divisible by 9, not just 3.

MISTAKE: Forgetting to add ALL digits, especially for larger numbers. | CORRECTION: Always ensure you add every single digit in the number to get the correct sum.

Practice Questions

Try It Yourself

QUESTION: Is 126 divisible by 9? | ANSWER: Yes

QUESTION: A cricket team scored 345 runs. Can these runs be divided equally among 9 players if each player scored the same whole number of runs? | ANSWER: No

QUESTION: Which of these numbers is divisible by 9: 504, 613, 720, 801? List all that apply. | ANSWER: 504, 720, 801

MCQ

Quick Quiz

Which of the following numbers is divisible by 9?

235

459

716

802

The Correct Answer Is:

For 459, the sum of digits is 4 + 5 + 9 = 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), 459 is divisible by 9. For other options, the sum of digits is not divisible by 9.

Real World Connection

In the Real World

When shopkeepers calculate discounts or GST (Goods and Services Tax) on items, they often need to quickly check if amounts are easily divisible. For example, if a shop offers a 9% discount on a bill, knowing divisibility by 9 helps in quick mental calculations to confirm the final amount, especially with digital payment apps like UPI.

Key Vocabulary

Key Terms

DIVISIBLE: Can be divided by another number without a remainder | REMAINDER: The amount left over after division | SUM: The result of adding numbers together | DIGITS: The individual symbols (0-9) that make up a number

What's Next

What to Learn Next

Great job learning about divisibility by 9! Next, you can explore "What is Divisibility by 11?" This rule is a bit different but equally fun and will further sharpen your number sense for bigger challenges!