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

Answer: (a)

$2/{2 + 2/{3 + 2 /{3 + {2/3}}}× {0.39}}$

= $2/{2 + 2/{3 + 2/{11/3}}× {0.39}}$

= $2/{2 + 2/{3 + {6/11}}× {0.39}}$

= $2/{2 + 2/{{33+6}/11}× {0.39}}$

= $2/{2 + {{11×2}/39} × {0.39}}$

= $2/{2 + {{11×2}/39} × {39/100}}$

= $2/{2+{11/50}} = 2/{{100+11}/50} = 100/111$

Answer: (b)

First part = ${30/7 - 1/2}/{7/2 + 8/7}$

= ${{60 - 7}/14}/{{49+16}/14} = {53/14} × 14/65 = 53/65$

Second part = $1/{2+1/{2+{1/{{25 - 1}/5}}}}$

= $1/{2+1/{2+{5/24}}} = 1/{2+{1/{{48+5}/24}}}$

= $1/{2+{24/53}} = 1/{{106+24}/53} = 53/130$

Expression = ${53/65} ÷ {53/130} = 53/65 × 130/53 = 2$

Answer: (a)

$2/{1+1/{1-{1/2}}} × 3/{{5/6} of {3/2} ÷ 1{1/4}}$

$2/{1+1/{1/2}} × 3/{({5/6 × 3/2}) ÷ {5/4}}$

= $2/{1 + 2} × 3/{{5/4}÷{5/4}}$

= $2/3×3/{{5/4}×{4/5}} = {2/3}×3 = 2$

Answer: (d)

? = $1+1/{1+2/{2+3/{1+{4/5}}}}$

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

= $1 + 1/{1 +{2 × 3}/{6 + 5}} = 1 + {1 × 11}/{11 + 6}$

= $1+11/17 = 1{11/17}$

Answer: (a)

Expression = $1 - a/{1-1/{1+{a/{1 - a}}}}$

= $1 - a/{1-{1/{{1 - a+a}/{1 - a}}}}$

= $1 - a/{1 - {1/{1/{1 - a}}}}$

= $1 - a/{1 - (1 - a)} = 1-a/{1 - 1+a}$

= 1 - 1 = 0