Model 4 Simplification with continued fraction Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (c)

$1 + 4/{2+3/{5-{1/2}}} - 1/2(10 ÷ 2)$

$1 + 4/{2+3/{{10 - 1}/2}} - 1/2(5)$

= $1 + 4/{2+{6/9}} - 5/2 = 1+4/{2 + {2/3}} - 5/2$

= $1 + 4/{8/3} - 5/2 = 1 + {4 × 3}/8 - 5/2$

= $1 +3/2 - 5/2 ={2 + 3 -5}/2 = 0$

Answer: (b)

$1+1/{1+{2/{{15+4}/5}}}$

= $1+1/{1+{{2×5}/19}} = 1+1/{{19+10}/19}$

= $1+{19/29} = {29+19}/29 = 48/29$

Answer: (a)

Expression = $1 + 1/{1 + {1/2}}$

= $1 + 1/{{2+1}/2} = 1+{2/3}$

= ${3 + 2}/3 = 5/3$

Answer: (c)

2 = $x+1/{1+1/{3+{1/4}}}$

2 = $x+1/{1+{1/{{12+1}/4}}}$

2 = $x+1/{1+{4/13}}$

2 = $x+1/{{13+4}/13}$

$2 = x + {1/{17/13}}$

2 = $x + 13/17 ⇒ x = 2 -{13/17}$

$= {34 - 13}/17 = 21/17$

Answer: (d)

? = $1 + 2/{1 + {{3 × 5}/9}} = 1 + 2/{1 + {5/3}}$

= $1 + {2 × 3}/8 = 7/4$