Question

1. \\(\frac{1}{2 + \frac{3}{4 + \frac{5}{6}}}\\) is equivalent to

(a) \\(\frac{29}{76}\\)
(b) \\(\frac{76}{29}\\)
(c) \\(\frac{20}{29}\\)
(d) \\(\frac{29}{20}\\)

Explanation:

Simplify the bottom-most fraction

Using the Fraction Addition knowledge point

$$ 4 + \frac{5}{6} = \frac{24}{6} + \frac{5}{6} = \frac{29}{6} $$

Simplify the next level denominator

Using the Fraction Division and Fraction Addition knowledge points

$$ 2 + \frac{3}{\frac{29}{6}} = 2 + 3 \cdot \frac{6}{29} = 2 + \frac{18}{29} = \frac{58}{29} + \frac{18}{29} = \frac{76}{29} $$

Evaluate the entire complex fraction

Using the Complex Fractions knowledge point

$$ \frac{1}{\frac{76}{29}} = \frac{29}{76} $$

Answer:

• (A) \(\frac{29}{76}\) (Correct answer)
• (B) \(\frac{76}{29}\)
• (C) \(\frac{20}{29}\)
• (D) \(\frac{29}{20}\)