Question 15

The fraction to be added to the fraction $$\frac{1}{2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{4}}}}$$ to get 1 is

Solution

Simplify from the bottom upwards. First $$1 + \frac{1}{4} = \frac{5}{4}$$, so the next step is $$3 + \frac{4}{5} = \frac{19}{5}$$, and then $$2 + \frac{5}{19} = \frac{43}{19}$$. The given fraction is therefore $$\frac{19}{43}$$, and the fraction to be added is $$1 - \frac{19}{43} = \frac{24}{43}$$.

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The fraction to be added to the fraction $$\frac{1}{2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{4}}}}$$ to get 1 is

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