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Basic Maths: Test 27

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Question 1
$ \frac{4\frac{9}{13}}{4+\frac{3}{3+\frac{1}{2}}}$
is equal to ?
A
1.7
B
1.5
C
2.4
D
0.96
Question 1 Explanation: 
We will solve this step by step
$ \begin{array}{l}\frac{\frac{61}{13}}{4+\frac{3}{3+\frac{1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{3}{\frac{6+1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{6}{7}}\\=\frac{\frac{61}{13}}{\frac{28+6}{7}}\\=\frac{61}{13}\times \frac{7}{34}=\frac{427}{442}=0.96\end{array}$
So the right answer for the question is option (d).
Question 2
$ \frac{9}{26}$ is equal to
A
$ \displaystyle \frac{1}{5+\frac{1}{7+\frac{1}{17}}}$
B
$ \displaystyle \frac{1}{2+\frac{1}{1+\frac{1}{8}}}$
C
$ \displaystyle \frac{1}{3+\frac{1}{1+\frac{1}{2+\frac{1}{4}}}}$
D
$ \displaystyle \frac{1}{16+\frac{1}{8+\frac{1}{2+\frac{1}{9}}}}$
Question 2 Explanation: 
The fraction can be written by hit and trail method
$ \begin{array}{l}\frac{1}{2+\frac{1}{1+\frac{1}{8}}}\\=\frac{1}{2+\frac{1}{\frac{8+1}{8}}}=\frac{1}{2+\frac{8}{9}}\\=\frac{1}{\frac{18+8}{9}}=\frac{9}{26}\end{array}$
Question 3
Simplyfy
$ 1+\frac{5}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}\,\left( 20\div 2 \right)$
A
-1/2
B
0
C
-17/8
D
1/3
Question 3 Explanation: 
$ \begin{array}{l}1+\frac{5}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}\,\times 10\\=1+\frac{5}{2+\frac{6}{9}}-5\\=1+\frac{5}{2+\frac{2}{3}}-5\\=1+\frac{5}{\frac{8}{3}}-5\\=1+\frac{5\times 3}{8}-5\\=\frac{15}{8}-4=\frac{15-32}{8}=\frac{-17}{8}\end{array}$
Question 4
$ \displaystyle \begin{array}{l}\frac{\left[ \left( 5+\frac{1}{9+\frac{1}{9}} \right)\times \left( 5+\frac{1}{9+\frac{1}{9}} \right)-\left( 5-\frac{1}{9+\frac{1}{9}} \right)\times \left( 5-\frac{1}{9+\frac{1}{9}} \right) \right]}{\left[ \left( 5+\frac{1}{9+\frac{1}{9}} \right)+\left( 5-\frac{1}{9+\frac{1}{9}} \right) \right]}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{array}$
A
$ \displaystyle \frac{40}{101}$
B
$ \displaystyle \frac{9}{41}$
C
$ \displaystyle \frac{21}{101}$
D
$ \displaystyle \frac{20}{100}$
Question 4 Explanation: 
We will solve this equation in sections
Let us consider first
Let us suppose
$ \begin{array}{l}5+\frac{1}{9+\frac{1}{9}}=\frac{419}{82}=a\\5-\frac{1}{9+\frac{1}{9}}=\frac{401}{82}=b.\\if\,you\,see\,\,it\,\,is\,\,a\,\,formula\,\,of\,\,\\\frac{{{a}^{2}}-{{b}^{2}}}{\left( a+b \right)}=\frac{\left( a+b \right)\left( a-b \right)}{\left( a+b \right)}\\=\left( a-b \right)\\=\frac{419}{82}-\frac{401}{82}=\frac{18}{82}=\frac{9}{41}\end{array}$
So the right answer for this question is option b
Question 5
$ 1+\frac{3}{2+\frac{1}{5}}=?$
A
$ \frac{26}{11}$
B
$ \frac{13}{6}$
C
$ \frac{15}{6}$
D
$ \frac{11}{26}$
Question 5 Explanation: 
The given fraction can be simplified by
Expression
$ =1+\frac{3}{2+\frac{1}{5}}$
$ =1+\frac{3}{2+\frac{1}{5}}=1+\frac{15}{11}=\frac{11+15}{11}=\frac{26}{11}$
Therefore the answer for the question is option a
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