Multiples Worksheets - 15 Worksheets Library - Free Printable

Problem: Solving the Multiples Worksheet

The worksheet asks us to identify which numbers are multiples of specific numbers or which are not. Let's solve each question step by step.

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#### Question 1: Which of the following numbers are multiples of 5?
- Numbers given: a) 15, b) 20, c) 12, d) 18, e) 35
- Multiples of 5: A number is a multiple of 5 if it ends in 0 or 5.
- 15: Ends in 5 → Multiple of 5
- 20: Ends in 0 → Multiple of 5
- 12: Does not end in 0 or 5 → Not a multiple of 5
- 18: Does not end in 0 or 5 → Not a multiple of 5
- 35: Ends in 5 → Multiple of 5

Answer: a) 15, b) 20, e) 35

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#### Question 2: Which of the following numbers are multiples of 8?
- Numbers given: a) 26, b) 24, c) 32, d) 45, e) 54
- Multiples of 8: A number is a multiple of 8 if it can be divided by 8 without leaving a remainder.
- 26 ÷ 8 = 3.25 (not an integer) → Not a multiple of 8
- 24 ÷ 8 = 3 (integer) → Multiple of 8
- 32 ÷ 8 = 4 (integer) → Multiple of 8
- 45 ÷ 8 = 5.625 (not an integer) → Not a multiple of 8
- 54 ÷ 8 = 6.75 (not an integer) → Not a multiple of 8

Answer: b) 24, c) 32

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#### Question 3: Which of the following numbers are multiples of 9?
- Numbers given: a) 21, b) 27, c) 36, d) 45, e) 29
- Multiples of 9: A number is a multiple of 9 if the sum of its digits is divisible by 9.
- 21: Sum of digits = 2 + 1 = 3 (not divisible by 9) → Not a multiple of 9
- 27: Sum of digits = 2 + 7 = 9 (divisible by 9) → Multiple of 9
- 36: Sum of digits = 3 + 6 = 9 (divisible by 9) → Multiple of 9
- 45: Sum of digits = 4 + 5 = 9 (divisible by 9) → Multiple of 9
- 29: Sum of digits = 2 + 9 = 11 (not divisible by 9) → Not a multiple of 9

Answer: b) 27, c) 36, d) 45

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#### Question 4: Which of the following numbers are not multiples of 5?
- Numbers given: a) 20, b) 21, c) 33, d) 39, e) 40
- Not multiples of 5: A number is not a multiple of 5 if it does not end in 0 or 5.
- 20: Ends in 0 → Multiple of 5
- 21: Does not end in 0 or 5 → Not a multiple of 5
- 33: Does not end in 0 or 5 → Not a multiple of 5
- 39: Does not end in 0 or 5 → Not a multiple of 5
- 40: Ends in 0 → Multiple of 5

Answer: b) 21, c) 33, d) 39

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#### Question 5: Which of the following numbers are not multiples of 7?
- Numbers given: a) 21, b) 28, c) 22, d) 35, e) 45
- Not multiples of 7: A number is not a multiple of 7 if it cannot be divided by 7 without leaving a remainder.
- 21 ÷ 7 = 3 (integer) → Multiple of 7
- 28 ÷ 7 = 4 (integer) → Multiple of 7
- 22 ÷ 7 = 3.14 (not an integer) → Not a multiple of 7
- 35 ÷ 7 = 5 (integer) → Multiple of 7
- 45 ÷ 7 = 6.43 (not an integer) → Not a multiple of 7

Answer: c) 22, e) 45

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#### Question 6: Which of the following numbers are multiples of both 3 and 6?
- Numbers given: a) 21, b) 24, c) 27, d) 30, e) 33
- Multiples of both 3 and 6: A number must be divisible by both 3 and 6. Since every multiple of 6 is also a multiple of 3, we only need to check divisibility by 6.
- 21 ÷ 6 = 3.5 (not an integer) → Not a multiple of 6
- 24 ÷ 6 = 4 (integer) → Multiple of 6
- 27 ÷ 6 = 4.5 (not an integer) → Not a multiple of 6
- 30 ÷ 6 = 5 (integer) → Multiple of 6
- 33 ÷ 6 = 5.5 (not an integer) → Not a multiple of 6

Answer: b) 24, d) 30

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#### Question 7: Which of the following numbers are multiples of both 5 and 10?
- Numbers given: a) 10, b) 15, c) 30, d) 35, e) 40
- Multiples of both 5 and 10: A number must be divisible by both 5 and 10. Since every multiple of 10 is also a multiple of 5, we only need to check divisibility by 10.
- 10 ÷ 10 = 1 (integer) → Multiple of 10
- 15 ÷ 10 = 1.5 (not an integer) → Not a multiple of 10
- 30 ÷ 10 = 3 (integer) → Multiple of 10
- 35 ÷ 10 = 3.5 (not an integer) → Not a multiple of 10
- 40 ÷ 10 = 4 (integer) → Multiple of 10

Answer: a) 10, c) 30, e) 40

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Final Answers:

1. a) 15, b) 20, e) 35
2. b) 24, c) 32
3. b) 27, c) 36, d) 45
4. b) 21, c) 33, d) 39
5. c) 22, e) 45
6. b) 24, d) 30
7. a) 10, c) 30, e) 40

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{a) 15, b) 20, e) 35} \\
2. \text{b) 24, c) 32} \\
3. \text{b) 27, c) 36, d) 45} \\
4. \text{b) 21, c) 33, d) 39} \\
5. \text{c) 22, e) 45} \\
6. \text{b) 24, d) 30} \\
7. \text{a) 10, c) 30, e) 40}
\end{array}
}
\]