Question : If $1 \frac{1}{3} \div \frac{2}{5} \times \frac{x}{5}=1 \frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$, then the value of $x$ is:
Option 1: 5.5
Option 2: 7.5
Option 3: 7.0
Option 4: 15
Correct Answer: 7.5
Solution : Given expression, $1 \frac{1}{3} \div \frac{2}{5} \times \frac{x}{5}=1 \frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$ ⇒ $\frac{4}{3} \div \frac{2}{5} \times \frac{x}{5}= \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6}$ Using the BODMAS Rule, B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction ⇒ $\frac43\times\frac52\times\frac{x}5=\frac{5}{4}\times\frac23\times6$ ⇒ $\frac{2x}{3}=5$ ⇒ $x=\frac{15}{2}=7.5$ Hence, the correct answer is 7.5
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Question : The value of $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$ is:
Option 1: $\frac{9}{8}$
Option 2: $\frac{9}{4}$
Option 3: $\frac{15}{32}$
Option 4: $\frac{89}{4}$
Question : What is the positive value of the following expression? $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-(8-11) \div(9 \times 5 \div 5 \text { of } 3)\}]}$
Option 1: $1 \frac{5}{6}$
Option 2: $1 \frac{1}{5}$
Option 3: $2 \frac{4}{5}$
Option 4: $2 \frac{3}{5}$
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{29}{6}$
Option 2: $\frac{17}{9}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{49}{12}$
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}-\frac{3}{4}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{25}{6}$
Option 2: $\frac{14}{3}$
Option 3: $\frac{17}{9}$
Question : The value of $\frac{5-[2+3(2-2 \times 2+5)-5] \div 5}{4 \times 4 \div 4 \text { of }(4+4 \div 4 \text { of } 4)}$ is:
Option 1: $3 \frac{3}{16}$
Option 2: $4 \frac{3}{80}$
Option 3: $\frac{2}{5}$
Option 4: $7 \frac{3}{5}$
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