Question

tell whether 55 is a multiple of 7.
select the correct choice below and, if necessary, fill in the answer box to your choice.
○ a. the number 55 is a multiple of 7 because 7 + \\(\square\\) = 55. (type a whole number.)
○ b. the number 55 is a multiple of 7 because 7 × \\(\square\\) = 55. (type a whole number.)
○ c. the number 55 is not a multiple of 7

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. So we need to check if there exists a whole number \( k \) such that \( 7\times k = 55 \), or if the concept of addition (as in option A) relates to being a multiple (it doesn't, since multiples are about multiplication).

Step2: Check option A

Option A suggests \( 7 + \square = 55 \). Solving for the square, we get \( \square=55 - 7=48 \). But being a multiple is not about addition, it's about multiplication. So option A is incorrect.

Step3: Check option B

Option B suggests \( 7\times\square = 55 \). Solving for \( \square \), we have \( \square=\frac{55}{7}\approx7.857 \), which is not a whole number. So there is no whole number \( k \) such that \( 7\times k = 55 \).

Step4: Conclusion

Since a multiple of 7 must be expressible as \( 7\times \) (a whole number), and 55 cannot be written in that form (because \( \frac{55}{7} \) is not a whole number), 55 is not a multiple of 7. So the correct option is the one that states 55 is not a multiple of 7 (assuming option C is "The number 55 is not a multiple of 7", even though it's cut off, the reasoning shows it's not a multiple).

Answer:

C. The number 55 is not a multiple of 7