# Basic Maths: Test 21

• This is an assessment test.
• These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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## Basic Maths: Test 21

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 Question 1
Find the value of
$\displaystyle \frac{1}{1+\frac{1}{1-\frac{1}{2}}}\times \frac{1}{\frac{5}{6}\,\,of\,\frac{3}{2}\div \,1\frac{1}{4}\,}$
 A 1/2 B 1/7 C 1/6 D 1/3
Question 1 Explanation:
The equation can be simplified as
$\displaystyle \begin{array}{l}\frac{1}{1+\frac{1}{\frac{1}{2}}}\times \frac{1}{\left( \frac{5}{6}\,\times \frac{3}{2} \right)\div \,\frac{5}{4}\,}\\=\frac{1}{1+2}\times \frac{1}{\frac{5}{4}\div \frac{5}{4}}\\=\frac{1}{3}\times \frac{1}{\frac{5}{4}\times \frac{4}{5}}\\=\frac{1}{3}\end{array}$
So the answer for the question is d
 Question 2
$\displaystyle \frac{1}{2+\frac{2}{3+\frac{2}{3+\frac{2}{3}}}\times 0.78}$ is simplified to
 A 7/3 B 100/11 C 111/100 D None of these
Question 2 Explanation:
$\displaystyle \begin{array}{l}\frac{1}{2+\frac{2}{3+\frac{2}{\frac{11}{3}}}\times 0.78}\\=\frac{1}{2+\frac{2}{3+\frac{6}{11}}\times 0.78}\\=\frac{1}{2+\frac{2}{\frac{33+6}{11}}\times 0.78}\\=\frac{1}{\begin{array}{l}2+\frac{11\times 2}{39}\times 0.78\\=\frac{1}{2+\frac{11\times 2}{39}\times \frac{78}{100}}\end{array}}\\=\frac{1}{2+\frac{11}{25}}\\=25/61\end{array}$
 Question 3
$\displaystyle 3+\frac{1}{1+\frac{1}{2}}$
is equal to
 A 3/5 B 3/2 C 11/3 D 7/3
Question 3 Explanation:
The Expression can be solved like as
$\displaystyle 3+\frac{1}{1+\frac{1}{2}}$
$\displaystyle \begin{array}{l}=3+\frac{1}{\frac{2+1}{2}}\\=3+\frac{2}{3}\\=\frac{9+2}{3}\\=\frac{11}{3}\end{array}$
 Question 4
The value of
$\displaystyle 5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}$ is
 A 134/21 B 132/23 C 143/21 D 118/21
Question 4 Explanation:
$\displaystyle \begin{array}{l}5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3+2}{3}}}}}\\\end{array}$
$\displaystyle \begin{array}{l}=5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5+3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{5}{8}}}\\=5+\frac{1}{1+\frac{1}{\frac{8+5}{8}}}\\=5+\frac{1}{1+\frac{8}{13}}=5+\frac{1}{\frac{13+8}{13}}\\=5+\frac{13}{21}=\frac{105+13}{21}=\frac{118}{21}\end{array}$
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