Let's evaluate each statement in the image to determine whether it is true or false:

1. If a number is divisible by 3, then it must also be divisible by 12.

• Analysis:
  • A number divisible by 3 does not necessarily mean it is divisible by 12.
  • For example, $9$ is divisible by 3 but not by 12.
• Answer: False

2. 13 divides 169.

• Analysis:
  • Check if $169 \div 13$ is an integer:
  • $169 \div 13 = 13$, which is an integer.
• Answer: True

3. 9 is a multiple of 27.

• Analysis:
  • To be a multiple, $27 \div 9$ must result in an integer:
  • $27 \div 9 = 3$, meaning $27$ is a multiple of $9$, not the other way around.
  • $9$ is not large enough to contain $27$ as a multiple.
• Answer: False

4. 55 divides 11.

• Analysis:
  • $55 \div 11 = 5$, so $55$ is a multiple of $11$, but the question asks if $55$ divides $11$.
  • $11 \div 55$ does not result in an integer.
• Answer: False

If you have any doubts about the reasoning, let me know!

Expanded Questions:

1. Can a number divisible by 12 always be divisible by 3? Why or why not?
2. What is the general rule to determine if one number divides another?
3. What is the difference between a "multiple" and a "factor" in mathematics?
4. Can a smaller number ever divide a larger number? Provide an example or reasoning.
5. Is $27$ a multiple of $9$? How does this relate to the concept of divisors?

Tip:

When determining divisibility, always divide the numbers and check for a whole number result.