(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 : \(\...
Question 1 Report
(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.
Answer Details
(a) Convert mixed numbers to improper fractions.
Numerator: \(4\tfrac{2}{9} - 1\tfrac{13}{15} = \tfrac{38}{9} - \tfrac{28}{15} = \tfrac{190}{45} - \tfrac{84}{45} = \tfrac{106}{45}\).
Denominator: First \(\tfrac{4}{7}\times 2\tfrac{1}{3} = \tfrac{4}{7}\times\tfrac{7}{3} = \tfrac{4}{3}\). Then \(2\tfrac{1}{5} + \tfrac{4}{3} = \tfrac{11}{5} + \tfrac{4}{3} = \tfrac{33}{15} + \tfrac{20}{15} = \tfrac{53}{15}\).
\(\dfrac{106/45}{53/15} = \dfrac{106}{45}\times\dfrac{15}{53} = \dfrac{106\times 15}{45\times 53} = \dfrac{2\times 15}{45} = \dfrac{30}{45} = \mathbf{\dfrac{2}{3}}\)
(b) Rationalise \(\dfrac{7\sqrt{5}}{\sqrt{7}}\) by multiplying by \(\dfrac{\sqrt{7}}{\sqrt{7}}\):
\(\dfrac{7\sqrt{5}}{\sqrt{7}}\times\dfrac{\sqrt{7}}{\sqrt{7}} = \dfrac{7\sqrt{35}}{7} = \mathbf{\sqrt{35}}\)
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