Solved Problems: Finding Multiples for Grade 6

📚 What are Multiples?

In mathematics, a multiple of a number is the result of multiplying that number by an integer (whole number). In simpler terms, it's like counting by that number. For example, multiples of 3 are 3, 6, 9, 12, and so on.

📜 A Little History

The concept of multiples has been around since ancient times. Early civilizations used multiples for tasks like dividing land, measuring time, and calculating trade. While the formal definition evolved over centuries, the fundamental idea of repeated addition remains the core of understanding multiples.

➗ Key Principles of Finding Multiples

• 🔢 Basic Multiplication: Understanding multiplication is the foundation. For example, $4 \times 5 = 20$, so 20 is a multiple of both 4 and 5.
• ➕ Repeated Addition: You can find multiples by repeatedly adding the same number. For instance, to find multiples of 2, start with 2, then add 2 to get 4, add 2 again to get 6, and so on.
• ♾️ Infinite Multiples: A number has an infinite number of multiples because you can keep multiplying it by larger and larger integers.
• 🎯 Divisibility: A number is a multiple of another if it can be divided by that number without leaving a remainder.

💡 Real-World Examples

Let's see how multiples pop up in everyday life:

• 🍪 Sharing Cookies: If you have 24 cookies and want to share them equally among 6 friends, you are using multiples of 6. 24 is a multiple of 6 because $6 \times 4 = 24$.
• 🗓️ Planning Events: If you need to buy snacks for a group of 8 people and each person gets 3 snacks, you need to find a multiple of 8. $8 \times 3 = 24$ snacks in total.
• ⏰ Time Management: Knowing multiples of 15 can help with scheduling. If a task takes 30 minutes, that's two 15-minute intervals, using the multiple of 15.

📝 Practice Quiz

Let's test your knowledge with some practice problems:

1. What are the first five multiples of 7?
2. Is 36 a multiple of 4? Why or why not?
3. List three multiples of 9 that are greater than 50 but less than 100.

Solutions:

1. 7, 14, 21, 28, 35
2. Yes, 36 is a multiple of 4 because $4 \times 9 = 36$.
3. 54, 63, 72, 81, 90, 99 (Any three of these are correct)

✅ Conclusion

Understanding multiples is crucial for various mathematical operations and everyday tasks. By grasping the basic principles and practicing regularly, you can master this fundamental concept. Keep exploring and practicing to build a strong foundation in math! Good luck!🍀