Divisibility Worksheet Answers: Quick Guide & Solutions
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Understanding divisibility is crucial for mastering the foundations of mathematics. Whether you are a student trying to grasp the concept or an educator looking for ways to teach it, having access to divisibility worksheet answers can make the learning process more efficient and effective. This article serves as a quick guide to divisibility, along with solutions to various problems typically found on worksheets. Let's dive into the essentials of divisibility!
What is Divisibility? 🤔
Divisibility refers to the ability of one integer to be divided by another integer without leaving a remainder. In simpler terms, if you can divide a number a by another number b and get a whole number (without fractions), then we say that a is divisible by b.
For example:
- 10 is divisible by 2 because ( 10 ÷ 2 = 5 ) (a whole number).
- 10 is not divisible by 3 because ( 10 ÷ 3 = 3.33 ) (not a whole number).
Key Divisibility Rules 📜
Here are some essential divisibility rules that can help you quickly determine if a number is divisible by another:
| Divisor | Divisibility Rule |
|---|---|
| 2 | A number is divisible by 2 if its last digit is even. |
| 3 | A number is divisible by 3 if the sum of its digits is divisible by 3. |
| 4 | A number is divisible by 4 if the last two digits form a number divisible by 4. |
| 5 | A number is divisible by 5 if its last digit is 0 or 5. |
| 6 | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 9 | A number is divisible by 9 if the sum of its digits is divisible by 9. |
| 10 | A number is divisible by 10 if its last digit is 0. |
Important Note: Always remember that these rules are tools to help you solve problems quickly, especially during tests.
Common Divisibility Problems 🧩
When working with divisibility worksheets, you’ll often encounter various types of problems. Here are a few common examples along with their solutions.
Example 1: Checking Divisibility
Problem: Determine if 144 is divisible by 12.
Solution:
- Calculate ( 144 ÷ 12 = 12 ).
- Since the result is a whole number, 144 is divisible by 12.
Example 2: Finding Divisors
Problem: List all the divisors of 30.
Solution:
- The divisors of 30 are all the numbers that can divide 30 without leaving a remainder.
- Divisors: 1, 2, 3, 5, 6, 10, 15, 30
Example 3: Using the Divisibility Rules
Problem: Is 258 divisible by 3?
Solution:
- Find the sum of the digits: ( 2 + 5 + 8 = 15 ).
- Since 15 is divisible by 3, 258 is also divisible by 3.
Example 4: Word Problems
Problem: A baker has 48 cookies. He wants to package them into boxes with 6 cookies each. How many boxes can he fill?
Solution:
- Calculate ( 48 ÷ 6 = 8 ).
- The baker can fill 8 boxes with 6 cookies each.
Example 5: Remainders
Problem: What is the remainder when 29 is divided by 5?
Solution:
- Calculate ( 29 ÷ 5 = 5 ) with a remainder of ( 4 ) because ( 5 × 5 = 25 ) and ( 29 - 25 = 4 ).
- The remainder is 4.
Practice Problems for Mastery 📝
To further reinforce your understanding of divisibility, try solving these practice problems:
- Is 72 divisible by 8?
- List all divisors of 36.
- Find the sum of the digits of 45. Is it divisible by 9?
- A farmer has 50 apples. How many boxes of 10 can he fill?
- What is the remainder when 37 is divided by 6?
Answers:
- Yes
- 1, 2, 3, 4, 6, 9, 12, 18, 36
- Sum is 9, Yes
- 5 boxes
- Remainder is 1
Conclusion: Embracing Divisibility 🚀
Mastering divisibility is not just a requirement for school; it’s a valuable life skill that enhances our ability to think critically and solve problems efficiently. By utilizing the rules of divisibility, understanding the concepts, and practicing regularly, anyone can gain confidence in math.
With this quick guide, you now have the resources needed to tackle divisibility problems and worksheets effectively. Keep practicing, and soon you'll find that numbers and their relationships become second nature!