Question : What is the value of $\frac{6}{13}[\frac{29}{12}+\frac{4}{18}(\frac{16}{12}+\frac{18}{9})–\frac{46}{15} \div \frac{23}{45}]$?
Option 1: $\frac{–312}{137}$
Option 2: $\frac{–307}{234}$
Option 3: $\frac{–294}{117}$
Option 4: $\frac{–207}{119}$
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Correct Answer: $\frac{–307}{234}$
Solution : $\frac{6}{13}[\frac{29}{12}+\frac{4}{18}(\frac{16}{12}+\frac{18}{9})–\frac{46}{15} \div \frac{23}{45}]$ $=\frac{6}{13}[\frac{29}{12}+\frac{4}{18}\times(\frac{48+72}{36})–\frac{46}{15} \div \frac{23}{45}]$ $=\frac{6}{13}[\frac{29}{12}+\frac{20}{27}–\frac{46}{15} \div \frac{23}{45}]$ $=\frac{6}{13}[\frac{29}{12}+\frac{20}{27}–6]$ $=\frac{6}{13}\times[\frac{261+80–648}{108}]$ $=\frac{6}{13}\times\frac{–307}{108}$ $=\frac{–307}{13\times18}$ $=\frac{–307}{234}$ Hence, the correct answer is $\frac{–307}{234}$.
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Question : What is the value of $\frac{(45 \times 3 \div 27 \times 4)(81 \div 5 \times 85 \div 51)}{(108 \div 18 \times 7\div21)(133 \times 3 \div 38 \times 4)} ?$
Option 1: $\frac{46}{7}$
Option 2: $\frac{45}{7}$
Option 3: $\frac{54}{7}$
Option 4: $\frac{39}{7}$
Question : The value of $14 \frac{4}{9}+16 \frac{5}{27}+2 \frac{5}{54}$ is:
Option 1: $32 \frac{17}{18}$
Option 2: $32 \frac{13}{18}$
Option 3: $31 \frac{13}{18}$
Option 4: $32 \frac{11}{18}$
Question : What is the value of $\frac{12 \times 4 \div 3 \text { of } 16+24-5}{46 \div 23 \times 2}$?
Option 1: 5
Option 2: 3
Option 3: 4
Option 4: 6
Question : What is the value of $\frac{196}{7} \div \frac{35}{12}$ of $\frac{132}{55} \times \frac{45}{20} ?$
Option 1: 45
Option 2: 36
Option 4: 9
Question : What is the value of $\frac{7}{11} \div \frac{21}{33} \times \frac{5}{12}+\frac{10}{36} \times \frac{6}{11} \div \frac{18}{33}$?
Option 1: $\frac{29}{35}$
Option 2: $\frac{25}{36}$
Option 3: $\frac{28}{39}$
Option 4: $\frac{24}{41}$
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