(a) Simplify : \(\frac{4\frac{2}{9} - 1\frac{13}{15}}{2\frac{1}{5} + \frac{4}{7} \times 2\frac{1}{3}}\) (b) By rationalising the denominator,...
(a) Simplify : \(\frac{4\frac{2}{9} - 1\frac{13}{15}}{2\frac{1}{5} + \frac{4}{7} \times 2\frac{1}{3}}\)
(b) By rationalising the denominator, simplify : \(\frac{7\sqrt{5}}{\sqrt{7}}\), leaving your answer in surd form.
Explanation
(a) \(\frac{4\frac{2}{9} - 1\frac{13}{15}}{2\frac{1}{5} + \frac{4}{7} \times 2\frac{1}{3}}\)
\(4\frac{2}{9} - 1\frac{13}{15} = \frac{38}{9} - \frac{28}{15}\)
= \(\frac{190 - 84}{45}\)
= \(\frac{106}{45}\)
\(2\frac{1}{5} + \frac{4}{7} \times 2\frac{1}{3} = \frac{11}{5} + (\frac{4}{7} \times \frac{7}{3})\)
= \(\frac{11}{5} + \frac{4}{3}\)
= \(\frac{33 + 20}{15}\)
= \(\frac{53}{15}\)
\(\therefore \frac{4\frac{2}{9} - 1\frac{13}{15}}{2\frac{1}{5} + \frac{4}{7} \times 2\frac{1}{3}} = \frac{106}{45} \div \frac{53}{15}\)
= \(\frac{106}{45} \times \frac{15}{53}\)
= \(\frac{2}{3}\)
(b) \(\frac{7\sqrt{5}}{\sqrt{7}}\)
= \(\frac{7\sqrt{5}}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}\)
= \(\frac{7\sqrt{35}}{7}\)
= \(\sqrt{35}\)