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WAEC Mathematics 2013 Paper

Question : 4

Total: 48

Simplify

\frac{ 1\frac{7}{8} \; \times \; 2\frac{2}{5} }{ 6 \; \frac{3}{4} \div \; \frac{3}{4} }

Solution:

Concept:

Convert mixed fractions to improper fractions, simplify numerator and denominator separately, then divide the results.

Explanation:

Simplify the numerator:

1\frac{7}{8} \times 2\frac{2}{5}

Convert to improper fractions:

1\frac{7}{8} = \frac{15}{8}

and

2\frac{2}{5} = \frac{12}{5}

So numerator

= \frac{15}{8} \times \frac{12}{5}

Cancel common factors:

= \frac{3 \times 3}{2 \times 1} = \frac{9}{2}

Simplify the denominator:

6\frac{3}{4} \div \frac{3}{4}

6\frac{3}{4} = \frac{27}{4}

, so denominator

= \frac{27}{4} \div \frac{3}{4} = \frac{27}{4} \times \frac{4}{3}

Cancel common factors:

= \frac{9}{1} = 9

Now divide the two results:

\frac{9}{2} \div 9

= \frac{9}{2} \times \frac{1}{9} = \frac{1}{2}

Answer:

\frac{1}{2}

(Option D).

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