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Basic Maths: Test 17

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Question 1
$\displaystyle \left[ 3\frac{1}{4}\div \left\{ 1\frac{1}{4}-\frac{1}{2}\left( 2\frac{1}{2}-\frac{1}{4}-\frac{1}{6} \right) \right\} \right]\,\div \left( \frac{1}{2}\,of\,4\frac{2}{3} \right)$
A
18.76
B
36.89
C
33.42
D
78.54
Question 1 Explanation:
image-20
Question 2
The value of $ \displaystyle 8\div \left[ 1+1\div \{1+1\div \left( 1+1\div 2 \right)\} \right]$ is
A
$ \displaystyle 1$
B
$ \displaystyle 5$
C
$ \displaystyle 2$
D
$ \displaystyle \frac{1}{2}$
Question 2 Explanation:
$ \displaystyle \begin{array}{l}=8\div \left[ 1+1\div \left\{ 1+1\div \left( 1+1\div 2 \right) \right\} \right]\\=8\div \left[ 1+1\div \left\{ 1+1\div \left( 1+\frac{1}{2} \right) \right\} \right]\\=8\div \left[ 1+1\div \left\{ 1+1\div \frac{3}{2} \right\} \right]\\=8\div \left[ 1+1\div \left\{ 1+\frac{2}{3} \right\} \right]\\=8\div \left[ 1+1\div \frac{5}{3} \right]\\=8\div \left[ 1+\frac{3}{5} \right]\\=8\div \frac{8}{5}=5\end{array}$
Question 3
The simplified value of  
$ \displaystyle \frac{\frac{1}{3}\div \frac{1}{3}\times \frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}\,of\,\frac{1}{3}}-\frac{1}{3}$
A
$ \displaystyle 0$
B
$ \displaystyle 1$
C
$ \displaystyle \frac{1}{3}$
D
$ \displaystyle -\frac{2}{9}$
Question 3 Explanation:
The given expression is
$ \displaystyle \begin{array}{l}=\frac{\frac{1}{3}\div \frac{1}{3}\times \frac{1}{3}}{\frac{1}{3}\div \left( \frac{1}{3}\,\times \,\frac{1}{3} \right)}-\frac{1}{3}\\=\frac{\frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}}-\frac{1}{3}\\=\frac{\frac{1}{3}}{\frac{1}{3}\times 9}-\frac{1}{3}\\=\frac{\frac{1}{3}}{3}-\frac{1}{3}\\=\frac{1}{9}-\frac{1}{3}=-2/9\end{array}$
Question 4
Simplify
$ \displaystyle \frac{2\frac{3}{4}}{1\frac{5}{6}}\div \frac{7}{8}\times \left( \frac{1}{3}+\frac{1}{4} \right)+\frac{5}{7}\div \frac{3}{4}\,\,of\,\frac{4}{7}$
A
$ \displaystyle \frac{56}{77}$
B
$ \displaystyle \frac{49}{80}$
C
$ \displaystyle 2\frac{2}{3}$
D
$ \displaystyle 3\frac{2}{9}$
Question 4 Explanation:
The given expression $ \displaystyle \begin{array}{l}\frac{\frac{11}{4}}{\frac{11}{6}}\div \frac{7}{8}\left( \frac{4+3}{12} \right)+\frac{5}{7}\div \frac{3}{4}\,\,of\,\,\frac{4}{7}\\=\left( \frac{11}{4}\times \frac{6}{11} \right)\div \frac{7}{8}\times \frac{7}{12}+\frac{5}{7}\div \left( \frac{3}{4}\times \frac{4}{7} \right)\\=\frac{3}{2}\div \frac{7}{8}\times \frac{7}{12}+\frac{5}{7}\div \frac{3}{7}\\=\frac{3}{2}\times \frac{8}{7}\times \frac{7}{12}+\frac{5}{7}\div \frac{3}{7}\\=1+\frac{5}{3}\\=\frac{8}{3}\\=2\frac{2}{3}\end{array}$
Question 5
The value of <br>$ \displaystyle \sqrt{4+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{49}}}}}$ <br>is
A
$ 2\sqrt{2}$
B
$ {2}/{\sqrt{2}}\;$
C
$ 7$
D
$ 5$
Question 5 Explanation:
image-21
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