Find the coefficient of m in the expression of ($\frac{m}{2} - 1 \frac{1}{2}$) (m + $\frac{2}{3}$)

Analyze the question: We need to expand (m/2 − 1½)(m + 2/3) and find the coefficient of m, which is the number multiplying m after collecting like terms.

Concept: Use FOIL (First, Outer, Inner, Last) to expand, then combine the m terms.

Solution:

Write 1½ as 3/2, so the expression is (m/2 − 3/2)(m + 2/3).

• First: (m/2)(m) = m²/2
• Outer: (m/2)(2/3) = m/3
• Inner: (−3/2)(m) = −3m/2
• Last: (−3/2)(2/3) = −1

Collect the m terms:

m/3 − 3m/2 = (2m − 9m)/6 = −7m/6

−7/6 = −1 1/6

So the expansion is m²/2 − (7/6)m − 1, and the coefficient of m is −7/6 = −1 1/6.

Answer: Option D, −1 1/6.

Tip: Convert mixed numbers to improper fractions before multiplying (1½ = 3/2). Then use a common denominator when combining the m terms. Mixed numbers inside brackets are a common source of errors.