Question

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the number 18 is a multiple of 6 because 6×□ = 18.
(type a whole number.)

b. the number 18 is a multiple of 6 because 6 + □ = 18.
(type a whole number.)

c. the number 18 is not a multiple of 6.

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 which option fits this definition.

Step2: Analyze Option A

For Option A, we have the equation \( 6\times\square = 18 \). To find \( \square \), we solve for \( \square \) by dividing both sides of the equation by 6: \( \square=\frac{18}{6} = 3 \), which is a whole number. This fits the definition of a multiple.

Step3: Analyze Option B

For Option B, the equation is \( 6+\square=18 \). Solving for \( \square \), we get \( \square = 18 - 6=12 \). But the definition of a multiple involves multiplication, not addition, so this is incorrect.

Step4: Analyze Option C

Since \( 6\times3 = 18 \), 18 is a multiple of 6, so Option C is incorrect.

Answer:

A. The number 18 is a multiple of 6 because \( 6\times\mathbf{3}=18 \).