Question

1. which descriptions of \\(\frac{12}{m} - 4\\) are correct if \\(m\\) is a nonzero number? choose all that apply

a. 12 more than the difference between \\(m\\) and 4
b. 4 less than the quotient of 12 and \\(m\\)
c. 4 less than the product of 12 and \\(m\\)
d. 4 less than the result of 12 divided by \\(m\\)
e. 4 more than the quotient of 12 and \\(m\\)

Explanation:

• Analyze Option A: The expression for "12 more than the difference between \( m \) and 4" would be \( (m - 4)+12=m + 8 \), which is not equal to \( \frac{12}{m}-4 \), so A is incorrect.
• Analyze Option B: The quotient of 12 and \( m \) is \( \frac{12}{m} \), and "4 less than" this quotient means subtracting 4 from \( \frac{12}{m} \), so the expression is \( \frac{12}{m}-4 \), so B is correct.
• Analyze Option C: The product of 12 and \( m \) is \( 12m \), and "4 less than" this product would be \( 12m - 4 \), which is not equal to \( \frac{12}{m}-4 \), so C is incorrect.
• Analyze Option D: "The result of 12 divided by \( m \)" is \( \frac{12}{m} \), and "4 less than" this result is \( \frac{12}{m}-4 \), so D is correct (this is the same reasoning as Option B, just phrased slightly differently).
• Analyze Option E: "4 more than the quotient of 12 and \( m \)" would be \( \frac{12}{m}+4 \), which is not equal to \( \frac{12}{m}-4 \), so E is incorrect.

Answer:

B. 4 less than the quotient of 12 and \( m \)
D. 4 less than the result of 12 divided by \( m \)