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WAEC Mathematics 2012 Paper

Question : 28

Total: 49

\frac{m}{2} - 1\frac{1}{2}

\frac{2}{3}

)

Solution:

Concept:

Expand the product and collect the terms containing

m

The coefficient of

m

is the constant factor multiplying

m

Explanation:

Convert the mixed fraction to an improper fraction:

1\frac{1}{2} = \frac{3}{2}

So the expression becomes:

\left(\frac{m}{2} - \frac{3}{2}\right)\left(m + \frac{2}{3}\right)

Use the distributive property to expand:

\frac{m}{2}(m) + \frac{m}{2}\left(\frac{2}{3}\right) - \frac{3}{2}(m) - \frac{3}{2}\left(\frac{2}{3}\right)

Simplify each term:

\frac{m^2}{2} + \frac{m}{3} - \frac{3m}{2} - 1

Collect the

m

-terms:

\frac{m}{3} - \frac{3m}{2} = \left(\frac{1}{3} - \frac{3}{2}\right)m

\frac{1}{3} - \frac{3}{2} = \frac{2 - 9}{6} = -\frac{7}{6}

So the

m

-term is

-\frac{7}{6}m

Answer:

D.\ -1\frac{1}{6}

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