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What is a Sequence of Multiples of a Number?
Grade Level:
Class 5
All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry
Definition
What is it?
A sequence of multiples of a number is a list of numbers you get by multiplying that number by 1, 2, 3, 4, and so on. It's like counting in steps, where each step is the size of the original number.
Simple Example
Quick Example
Imagine you are buying samosas, and each samosa costs 10 rupees. If you buy 1 samosa, you pay 10 rupees. If you buy 2, you pay 20 rupees. If you buy 3, you pay 30 rupees. The amounts you pay (10, 20, 30, ...) form a sequence of multiples of 10.
Worked Example
Step-by-Step
Let's find the first 5 multiples of 7.
Step 1: To find the first multiple, multiply 7 by 1.
7 x 1 = 7
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Step 2: To find the second multiple, multiply 7 by 2.
7 x 2 = 14
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Step 3: To find the third multiple, multiply 7 by 3.
7 x 3 = 21
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Step 4: To find the fourth multiple, multiply 7 by 4.
7 x 4 = 28
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Step 5: To find the fifth multiple, multiply 7 by 5.
7 x 5 = 35
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Answer: The first 5 multiples of 7 are 7, 14, 21, 28, 35.
Why It Matters
Understanding sequences of multiples helps you with multiplication tables and division. This concept is important in finance for calculating interest, in computer science for algorithms, and even in physics for understanding patterns in waves. Many careers, from a banker to a software developer, use these basic number patterns.
Common Mistakes
MISTAKE: Confusing multiples with factors. For example, thinking 3 is a multiple of 6. | CORRECTION: Multiples are numbers you get by multiplying, so 6, 12, 18 are multiples of 6. Factors are numbers that divide evenly into another number, so 1, 2, 3, 6 are factors of 6.
MISTAKE: Forgetting that the number itself is its first multiple. For example, listing the multiples of 5 as 10, 15, 20... | CORRECTION: The first multiple of any number is the number multiplied by 1. So, the first multiple of 5 is 5 (5 x 1).
MISTAKE: Listing numbers that are not exact multiples. For example, for multiples of 4, listing 4, 8, 10, 12... | CORRECTION: Always check if the number can be divided exactly by the original number. 10 cannot be divided exactly by 4, so it's not a multiple.
Practice Questions
Try It Yourself
QUESTION: Write down the first 4 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 equals 48 (6 x 8 = 48).
QUESTION: A bus leaves the station every 15 minutes. If the first bus leaves at 6:00 AM, what are the next three times a bus will leave? | ANSWER: 6:15 AM, 6:30 AM, 6:45 AM
MCQ
Quick Quiz
Which of these numbers is NOT a multiple of 8?
16
24
30
40
The Correct Answer Is:
C
30 is not a multiple of 8 because 30 cannot be divided exactly by 8. 16 (8x2), 24 (8x3), and 40 (8x5) are all multiples of 8.
Real World Connection
In the Real World
Think about planning your day using a train timetable. If a train to Mumbai leaves every 2 hours, starting at 7:00 AM, the departure times (7:00 AM, 9:00 AM, 11:00 AM, etc.) form a sequence of multiples of 2 hours. This helps you know when to reach the station.
Key Vocabulary
Key Terms
MULTIPLE: The result of multiplying a number by an integer. | SEQUENCE: An ordered list of numbers. | PRODUCT: The result of multiplication. | DIVISIBLE: Able to be divided by another number without a remainder.
What's Next
What to Learn Next
Great job understanding sequences of multiples! Next, you can explore 'Least Common Multiple (LCM)'. It builds directly on this concept and helps you find the smallest number that is a multiple of two or more different numbers.
