Question : Simplify: $5 \frac{1}{3}-\left\{4 \frac{1}{3}+\left(3 \frac{1}{3} \div \overline{2 \frac{1}{3}-\frac{1}{3}}\right)\right\}$
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{3}$
Option 3: $-\frac{1}{3}$
Option 4: $-\frac{2}{3}$
Correct Answer: $-\frac{2}{3}$
Solution : $5 \frac{1}{3}-\left\{4 \frac{1}{3}+\left(3 \frac{1}{3} \div \overline{2 \frac{1}{3}-\frac{1}{3}}\right)\right\}$ $=\frac{16}{3}-\left\{ \frac{13}{3}+\left( \frac{10}{3} \div \overline{\frac{7}{3}-\frac{1}{3}}\right)\right\}$ $=\frac{16}{3}-\left\{ \frac{13}{3}+\left( \frac{10}{3} \div 2\right)\right\}$ $=\frac{16}{3}-\left\{ \frac{13}{3}+( \frac{5}{3})\right\}$ $=-\frac{2}{3}$ Hence, the correct answer is $-\frac{2}{3}$.
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Question : Solve the following. $\frac{24 \div \frac{3}{8} \text { of }(8+2 \times \overline{7-3})+\left[\frac{2}{11} \div \frac{4}{55}-\left\{\frac{5}{8}+\frac{6}{16}\right\}\right]}{32 \div \overline{15-7}+75 \div(6+15 \div 3+4)} $
Option 1: $\frac{23}{27}$
Option 2: $\frac{9}{2}$
Option 3: $\frac{11}{18}$
Option 4: $\frac{15}{19}$
Question : The value of $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}+\left(2 \div 2\right.$ of $\left.\frac{1}{2}\right)$ is:
Option 1: $\frac{7}{2}$
Option 2: $3$
Option 3: $5$
Option 4: $\frac{9}{4}$
Question : The value of $1 \frac{2}{5}-\left[3 \frac{3}{4} \div\left\{1 \frac{1}{4} \div \frac{1}{2}\left(1 \frac{1}{2} \times 3 \frac{1}{3} \div 1 \frac{1}{3}\right)\right\}\right]$ is:
Option 1: 3
Option 2: 0
Option 3: 2
Option 4: 1
Question : The value of $\left[1 \frac{2}{7} \times\left\{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right\}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{3}{4}$
Option 3: $2$
Option 4: $1$
Question : The value of $\left(5 \div 2\right.$ of $\left.\frac{1}{2}\right)+\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}$ is:
Option 1: $\frac{35}{24}$
Option 2: $8$
Option 3: $\frac{15}{28}$
Option 4: $–2$
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