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

Answer: (b)

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

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

= $1 + 1/{1 + {1/{5/3}}} = 1 + 1/{1+{3/5}}$

= $1 + 1/{8/5} = 1 + {5/8} = 13/8$

$2x + 7/4 = 2 ×13/8 + 7/4$

= ${13 + 7}/4 = 20/4 =5$

Answer: (d)

Let, $a=1+{1/{10+{1/10}}}$

= $1+1/{{100+1}/10} = 1+{10/101}$

= ${101+10}/101 = 111/101$

Again,

$b=1-{1/{10+{1/10}}} = 1 - 1/{{100+1}/10}$

= $1 - 10/101$

= ${101 - 10}/101 = 91/101$

Expression = $(a^2 - b^2)÷ab$

= ((a+b)(a - b))÷ab

= $({111/101} + 91/101)(111/101 - {91/101})$

÷ $(111/101 × 91/101)$

= $202/101 × 20/101 × {101×101}/{111×91}$

= $4040/{10101}$

Answer: (d)

${19/43}÷{1/{2+1/{3+1/{1+{1/4}}}}}$

= ${19/43}÷{1/{2+1/{3+{4/5}}}}$

= ${19/43}÷{1/{2+{5/19}}} = {19/43}÷ {19/43}$

= ${19/43}×{43/19}$ = 1

Answer: (d)

Expression

= ${{7/3} - {13/11}}/{3+1/{3+1/{{9+1}/3}}} = {{77-39}/33}/{3+1/{3+{3/10}}}$

= ${38/33}/{3+{1/{{30+3}/10}}}= {38/33}/{3+{10/33}}$

= ${38/33}/{{99+10}/33} = {38/33} × {33/109} = {38/109}$

Answer: (d)

${79/14}/{5 + 3/{3 + {5/3}}}$

= ${79/14}/{5 + 3/{{9 + 5}/3}}$

= ${79/14}/{5 + {9/14}} = {79/14}/{{70 + 9}/14}$

= $79/14 × 14/79 = 1$