JAMB 2004 · UME · Q3

Simplify $\dfrac{\frac1{10} \times \frac23 + \frac14}{\frac12 \div \frac35 - \frac14}$ .

Worked solution (try it first)

Top: multiply first, $\frac{1}{10} \times \frac23 = \frac{1}{15}$ .
Then $\frac{1}{15} + \frac14 = \frac{4}{60} + \frac{15}{60}$
$= \frac{19}{60}$ .
Bottom: divide first by flipping, $\frac12 \div \frac35 = \frac12 \times \frac53$
$= \frac56$ .
Then $\frac56 - \frac14 = \frac{10}{12} - \frac{3}{12}$
$= \frac{7}{12}$ .
Top divided by bottom: $\frac{19}{60} \times \frac{12}{7} = \frac{19}{35}$ , option D.