m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) and n : q = \(1\frac{1}{2} : 1\frac{1}{3}\), find q : m.
m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) = m : n = \(\frac{7}{3} : \frac{6}{5}\)
\(\frac{7}{3} : \frac{6}{5}\) = \(\frac{7}{3} \div \frac{6}{5}\)
\(\frac{m}{n}\) = \(\frac{7}{3} \times \frac{5}{6}\)
\(\frac{m}{n}\) = \(\frac{35}{18}\) = m = \(\frac{35n}{18}\)
n : q = \(1\frac{1}{2} : 1\frac{1}{3}\) = \(\frac{3}{2} : \frac{4}{3}\)
\(\frac{n}{q}\) = \(\frac{3}{2} \times\frac{3}{4}\)
\(\frac{n}{q}\) = \(\frac{9}{8}\) = q = \(\frac{8n}{9}\)
q : m = \(\frac{8n}{9}\) : \(\frac{35n}{18}\)
\(\frac{q}{m}\) = \(\frac{8n}{9} \div \frac{35n}{18}\)
\(\frac{q}{m}\) = \(\frac{8n}{9}\times\frac{18}{35n}\)
=\(\frac{q}{m} = \frac{16}{35}\) = q : m = 16 : 35
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