Question
Without using your calculator, work out \(\frac{3}{8}\div 2\frac{1}{4}\)
You must show all your working and give your answer as a fraction in its simplest form.
Answer/Explanation
\(\frac{3}{8}\times \frac{4}{9}\) or \(\frac{3}{8}\div \frac{18}{8}\) with common denominator \(\frac{1}{6}\)
Question
Seismic shock waves travel at speed v through rock of density d.
v varies inversely as the square root of d.
v = 3 when d = 2.25.
Find v when d = 2.56.
Answer/Explanation
Since, \(V\alpha\frac{1}{\sqrt{d}}\)
\(\Rightarrow V=K.\frac{1}{\sqrt{d}}\)(K is constant of propotionality)—(i)
Given, V=3
d=2.25
Putting these values in the equation(i):
3=K.\(\sqrt{\frac{100}{225}}\)
3=K.\(\frac{10}{15}\)
\(\Rightarrow K=\frac{9}{2}\)
Now, V=?
d=2.56
Using, equation (i)
\(V=\frac{9}{2}\sqrt{\frac{1}{2.56}}\)
Now, \(V=\frac{9}{2}\sqrt{\frac{100}{256}}\)
\(V=\frac{9}{2}\times\frac{10}{16}\)
\(\frac{45}{16}\)
=2.81
Question
Reina went on holiday to New Zealand.
(a) She travelled the 65 km from Tokyo to Narita Airport by taxi. The taxi journey cost 300 yen (¥) per kilometre plus a fixed charge of ¥ 700. Calculate the cost of the taxi journey.
(b) At Narita Airport, Reina changed ¥ 71 190 into New Zealand dollars (NZ$). The exchange rate was NZ$1 = ¥ 56.5. How many New Zealand dollars did she receive?
▶️Answer/Explanation
(a) 20200
(b) 1260