Question

7.5.ap-19
tell whether 58 is a multiple of 3.
select the correct choice below and, if necessary, fill in the ans your choice.
a. the number 58 is a multiple of 3 because 3×□ = 58. (type a whole number.)
b. the number 58 is a multiple of 3 because 3 + □ = 58.

Explanation:

Step1: Recall multiple definition

A multiple of a number \( n \) is a number \( m \) such that \( m = n\times k \) for some whole number \( k \). For 58 to be a multiple of 3, there must exist a whole number \( k \) where \( 3\times k = 58 \).

Step2: Check divisibility by 3

We can also use the divisibility rule for 3: the sum of digits of a number is divisible by 3 if the number is divisible by 3. The sum of digits of 58 is \( 5 + 8=13 \), and 13 is not divisible by 3. So 58 is not divisible by 3, meaning there is no whole number \( k \) such that \( 3\times k = 58 \). Also, the concept of a multiple is about multiplication, not addition, so option B is incorrect. Since there's no whole number \( k \) with \( 3\times k = 58 \), 58 is not a multiple of 3. But looking at the options, we need to analyze them. Option A's equation \( 3\times k = 58 \) has no whole number solution (since \( 58\div3=\frac{58}{3}\approx19.33 \), not a whole number), and option B is wrong because multiples are about multiplication, not addition. However, the question seems to have a typo or missing options, but based on the divisibility, 58 is not a multiple of 3. But if we have to choose between A and B, both are wrong, but since the problem is about multiples (multiplication), A is the form for multiples, but it's incorrect. But maybe the original problem had a third option (like C: 58 is not a multiple of 3), but since it's not shown, but based on the given options, neither A nor B is correct, but if we follow the options, we can see that 58 is not a multiple of 3, so neither A nor B is correct. But since the user provided the options as A and B, maybe there's a mistake. But to answer, 58 is not a multiple of 3, so neither A nor B is correct. But if we have to choose, the correct answer is that neither A nor B is correct, but since the options are given as A and B, maybe the problem intended to have a correct option, but there's an error. However, based on the mathematical definition, a multiple of 3 is a number that can be written as \( 3\times k \) where \( k \) is a whole number. Since \( 58\div3 \) is not a whole number, 58 is not a multiple of 3, so both A and B are incorrect. But since the user's options are A and B, maybe there's a mistake in the problem. But if we have to proceed, the answer is that 58 is not a multiple of 3, so neither A nor B is correct. But since the options are given, perhaps the intended answer is that neither is correct, but since the options are A and B, maybe the problem has an error. However, based on the calculation, \( 3\times19 = 57 \) and \( 3\times20 = 60 \), so 58 is between them, not a multiple of 3.

Answer:

Neither A nor B is correct (since \( 3\times k = 58 \) has no whole number solution and multiples are about multiplication, not addition). But if forced to choose between A and B, both are incorrect. However, if the problem had a third option (e.g., C: 58 is not a multiple of 3), that would be correct.