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