Which of the following represents the correct simplified value of the continued fraction: \(x = 1 + \cfrac{1}{2 + \cfrac{1}{2 + \tfrac{1}{2}}}\)
\(\dfrac{17}{12}\)
Work from the inside out.
Step 1 – Innermost: \(2 + \tfrac{1}{2} = \dfrac{5}{2}\)
Step 2 – Next layer: \(2 + \dfrac{1}{\,5/2\,} = 2 + \dfrac{2}{5} = \dfrac{12}{5}\)
Step 3 – Outermost: \(x = 1 + \dfrac{1}{\,12/5\,} = 1 + \dfrac{5}{12} = \dfrac{17}{12}\)
Hence \(x = \dfrac{17}{12}\).
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Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
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d.
\(\frac{19}{5}\) is
iv.
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