Question

tell whether 11 is a multiple of 3.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the number 11 is a multiple of 3 because 3 + \\(\square\\) = 11. (type a whole number.)
b. the number 11 is a multiple of 3 because 3 × \\(\square\\) = 11. (type a whole number.)

Explanation:

Step1: Recall the definition of a multiple

A multiple of a number \( n \) is a number that can be expressed as \( n\times k \) where \( k \) is a whole number. For 3, a multiple should satisfy \( 3\times k = m \) (where \( m \) is the multiple).

Step2: Analyze Option A

Option A suggests \( 3 + \square=11 \). Solving for \( \square \), we get \( \square = 11 - 3=8 \). But being a multiple is about multiplication, not addition. So A is incorrect.

Step3: Analyze Option B

Option B suggests \( 3\times\square = 11 \). Solving for \( \square \), we get \( \square=\frac{11}{3}\approx3.67 \), which is not a whole number. Since a multiple of 3 must be \( 3\times k \) with \( k \) a whole number, 11 is not a multiple of 3. So neither A nor B is correct (but since we have to choose from A or B, and both are wrong in their reasoning, but the question is to tell if 11 is a multiple. But based on the options, the correct conclusion is that 11 is not a multiple, but since the options are A and B (both incorrect in their reasoning), but if we have to check the options:

For A: The reasoning is wrong (multiple is multiplication, not addition). For B: \( \frac{11}{3} \) is not a whole number, so 11 is not a multiple of 3. But the question's options are flawed, but if we have to answer based on the options, neither A nor B is correct, but since the problem is to tell if 11 is a multiple, and the answer is no, but the options are A and B (both wrong). However, the correct mathematical conclusion is that 11 is not a multiple of 3. But since the options are given, we can see that both A and B are incorrect in their reasoning. But if we have to choose from A or B, neither is correct, but the problem might have a typo. But based on the definition, a multiple of 3 is \( 3, 6, 9, 12, \dots \), so 11 is not a multiple.

Answer:

11 is not a multiple of 3. (Neither A nor B is correct as A uses addition (multiple is about multiplication) and B gives a non - whole number. But if we have to choose from A and B, there is no correct option. However, the mathematical answer is that 11 is not a multiple of 3.)