What is a Multiple?

S3-SA4-0027

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A multiple of a number is the result you get when you multiply that number by any whole number (like 1, 2, 3, 4, and so on). Think of it as counting by that number repeatedly. For example, multiples of 2 are 2, 4, 6, 8, and so on.

Simple Example

Quick Example

Imagine you are buying samosas, and each samosa costs Rs. 10. If you buy 1 samosa, you pay Rs. 10. If you buy 2, you pay Rs. 20. If you buy 3, you pay Rs. 30. Here, 10, 20, 30 are all multiples of 10, because you get them by multiplying 10 by 1, 2, 3, etc.

Worked Example

Step-by-Step

Let's find the first five multiples of 7.
---Step 1: To find the first multiple, multiply 7 by 1.
7 x 1 = 7
---Step 2: To find the second multiple, multiply 7 by 2.
7 x 2 = 14
---Step 3: To find the third multiple, multiply 7 by 3.
7 x 3 = 21
---Step 4: To find the fourth multiple, multiply 7 by 4.
7 x 4 = 28
---Step 5: To find the fifth multiple, multiply 7 by 5.
7 x 5 = 35
---Answer: The first five multiples of 7 are 7, 14, 21, 28, and 35.

Why It Matters

Understanding multiples is super important for many cool fields! In Computer Science, multiples help in scheduling tasks or arranging data efficiently. Engineers use multiples when designing gears or setting up production lines. Even AI/ML algorithms use similar concepts for pattern recognition, making your favorite apps smarter!

Common Mistakes

MISTAKE: Thinking a number is a multiple of itself only if it's multiplied by a number greater than 1. For example, thinking 5 is not a multiple of 5. | CORRECTION: Every number is a multiple of itself, because any number multiplied by 1 gives itself. So, 5 x 1 = 5, making 5 a multiple of 5.

MISTAKE: Confusing multiples with factors. For example, saying 2 is a multiple of 10. | CORRECTION: Multiples are always equal to or larger than the original number (unless multiplied by zero). Factors are numbers that divide the original number exactly. 10 is a multiple of 2, but 2 is a factor of 10.

MISTAKE: Forgetting that multiples go on infinitely. For example, thinking the multiples of 3 stop at 30. | CORRECTION: Multiples of any number are endless because you can keep multiplying it by larger and larger whole numbers (3 x 1, 3 x 2, 3 x 3, ... 3 x 100, ... and so on).

Practice Questions

Try It Yourself

QUESTION: List the first four multiples of 9. | ANSWER: 9, 18, 27, 36

QUESTION: Is 48 a multiple of 6? Explain why. | ANSWER: Yes, 48 is a multiple of 6 because 6 multiplied by 8 gives 48 (6 x 8 = 48).

QUESTION: Find a number that is a multiple of both 4 and 5. | ANSWER: 20 (because 4 x 5 = 20, and 5 x 4 = 20. Other answers like 40, 60 are also correct.)

MCQ

Quick Quiz

Which of these numbers is NOT a multiple of 8?

The Correct Answer Is:

16 (8x2), 32 (8x4), and 48 (8x6) are all multiples of 8. 50 is not a multiple of 8 because 8 does not divide 50 exactly (50 divided by 8 leaves a remainder).

Real World Connection

In the Real World

Think about scheduling a train or bus. If a bus comes every 15 minutes, the arrival times (like 9:00 AM, 9:15 AM, 9:30 AM, 9:45 AM) are all multiples of 15 minutes from the starting time. This helps passengers and transport companies plan routes and travel times efficiently across India.

Key Vocabulary

Key Terms

MULTIPLE: The result of multiplying a number by a whole number | WHOLE NUMBER: Numbers like 0, 1, 2, 3, and so on (no fractions or decimals) | PRODUCT: The answer when two or more numbers are multiplied together | DIVISIBLE: Able to be divided by another number without a remainder

What's Next

What to Learn Next

Great job understanding multiples! Now that you know what multiples are, you're ready to learn about 'Least Common Multiple' (LCM). LCM helps you find the smallest multiple that two or more numbers have in common, which is super useful in solving problems with fractions!