Students can use this worksheet to practice identifying multiples of various numbers and answering conceptual questions.

Problem Explanation and Solution:

The worksheet focuses on understanding multiples of numbers. Let's solve each question step by step.

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#### 1. What are the first 4 multiples of 9?

A multiple of a number is obtained by multiplying that number by any whole number (1, 2, 3, etc.). To find the first 4 multiples of 9, we multiply 9 by the first 4 whole numbers:

- \( 9 \times 1 = 9 \)
- \( 9 \times 2 = 18 \)
- \( 9 \times 3 = 27 \)
- \( 9 \times 4 = 36 \)

Thus, the first 4 multiples of 9 are: 9, 18, 27, 36.

Answer: 9, 18, 27, 36

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#### 2. Circle the numbers that are multiples of 7. Cross out the numbers that are not multiples of 7.

We are given the numbers: 1, 7, 14, 17, 21, 27, 35. To determine which of these are multiples of 7, we check if each number can be divided by 7 without leaving a remainder.

- 1: Not a multiple of 7 (1 ÷ 7 ≠ whole number).
- 7: Multiple of 7 (7 ÷ 7 = 1).
- 14: Multiple of 7 (14 ÷ 7 = 2).
- 17: Not a multiple of 7 (17 ÷ 7 ≠ whole number).
- 21: Multiple of 7 (21 ÷ 7 = 3).
- 27: Not a multiple of 7 (27 ÷ 7 ≠ whole number).
- 35: Multiple of 7 (35 ÷ 7 = 5).

So, the multiples of 7 are: 7, 14, 21, 35.

Answer: Circle: 7, 14, 21, 35; Cross out: 1, 17, 27.

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#### 3. Circle the numbers that are multiples of 8. Cross out the numbers that are not multiples of 8.

We are given the numbers: 38, 40, 45, 49, 64, 72, 81. To determine which of these are multiples of 8, we check if each number can be divided by 8 without leaving a remainder.

- 38: Not a multiple of 8 (38 ÷ 8 ≠ whole number).
- 40: Multiple of 8 (40 ÷ 8 = 5).
- 45: Not a multiple of 8 (45 ÷ 8 ≠ whole number).
- 49: Not a multiple of 8 (49 ÷ 8 ≠ whole number).
- 64: Multiple of 8 (64 ÷ 8 = 8).
- 72: Multiple of 8 (72 ÷ 8 = 9).
- 81: Not a multiple of 8 (81 ÷ 8 ≠ whole number).

So, the multiples of 8 are: 40, 64, 72.

Answer: Circle: 40, 64, 72; Cross out: 38, 45, 49, 81.

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#### 4. Are multiples of 4 always even? Explain.

To determine if multiples of 4 are always even, let’s consider the definition of even numbers and multiples.

- An even number is any integer that is divisible by 2.
- A multiple of 4 is any number that can be written as \( 4 \times n \), where \( n \) is an integer.

Since \( 4 = 2 \times 2 \), any multiple of 4 can be written as:
\[ 4 \times n = (2 \times 2) \times n = 2 \times (2 \times n) \]

This shows that any multiple of 4 is also a multiple of 2, meaning it is always divisible by 2. Therefore, multiples of 4 are always even.

Answer: Yes, multiples of 4 are always even because they can be expressed as \( 2 \times (2 \times n) \), which is always divisible by 2.

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#### 5. Are multiples of 3 always odd? Explain.

To determine if multiples of 3 are always odd, let’s consider the definition of odd numbers and multiples.

- An odd number is any integer that is not divisible by 2.
- A multiple of 3 is any number that can be written as \( 3 \times n \), where \( n \) is an integer.

Multiples of 3 can be either odd or even, depending on the value of \( n \):
- If \( n \) is odd, \( 3 \times n \) is odd (e.g., \( 3 \times 1 = 3 \), \( 3 \times 3 = 9 \)).
- If \( n \) is even, \( 3 \times n \) is even (e.g., \( 3 \times 2 = 6 \), \( 3 \times 4 = 12 \)).

Since multiples of 3 can be both odd and even, they are not always odd.

Answer: No, multiples of 3 are not always odd because they can be even (e.g., 6, 12, 18).

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Final Answers:

1. 9, 18, 27, 36
2. Circle: 7, 14, 21, 35; Cross out: 1, 17, 27
3. Circle: 40, 64, 72; Cross out: 38, 45, 49, 81
4. Yes, multiples of 4 are always even because they can be expressed as \( 2 \times (2 \times n) \), which is always divisible by 2.
5. No, multiples of 3 are not always odd because they can be even (e.g., 6, 12, 18).

Boxed Final Answer:
\[
\boxed{9, 18, 27, 36}
\]
\[
\boxed{\text{Circle: 7, 14, 21, 35; Cross out: 1, 17, 27}}
\]
\[
\boxed{\text{Circle: 40, 64, 72; Cross out: 38, 45, 49, 81}}
\]
\[
\boxed{\text{Yes, multiples of 4 are always even because they can be expressed as } 2 \times (2 \times n), \text{ which is always divisible by 2.}}
\]
\[
\boxed{\text{No, multiples of 3 are not always odd because they can be even (e.g., 6, 12, 18).}}
\]