Question

7.5.ap-11
tell whether 23 is a multiple of 4.
select the correct choice below and, if necessary, fill in the answer your choice.
a. the number 23 is a multiple of 4 because 4×□=23.
(type a whole number.)
b. the number 23 is a multiple of 4 because 4+□=23.

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, to check if 23 is a multiple of 4, we need to see if there exists a whole number \( k \) such that \( 4\times k = 23 \).

Step2: Solve for \( k \)

We solve the equation \( 4\times k = 23 \) for \( k \). Dividing both sides by 4, we get \( k=\frac{23}{4} = 5.75 \). Since \( 5.75 \) is not a whole number, there is no whole number \( k \) such that \( 4\times k = 23 \). Also, the concept of a multiple is about multiplication, not addition, so option B is incorrect as well. So 23 is not a multiple of 4. But since the options given are trying to assert it is, both A and B are wrong, but based on the definition, we check the multiplication. Since \( \frac{23}{4} \) is not a whole number, option A's box can't be filled with a whole number, so 23 is not a multiple of 4. But if we have to address the options, the correct reasoning is that there's no whole number \( k \) for \( 4\times k = 23 \), so 23 is not a multiple of 4. However, since the problem's options are flawed in their assertion, but following the process, we see that \( 4\times5 = 20 \) and \( 4\times6=24 \), so 23 is between them, not a multiple.

Answer:

23 is not a multiple of 4. (But if we have to comment on the options, neither A nor B is correct because there is no whole number \( k \) such that \( 4\times k = 23 \) (for A) and multiple is defined by multiplication not addition (for B). However, if forced to choose based on the wrong options, the answer is that there is no valid whole number for A, so 23 is not a multiple of 4.)