Question : The greatest fraction among $\frac{2}{3}, \frac{5}{6}, \frac{11}{15} \text{ and } \frac{7}{8} \text{ is:}$
Option 1: $\frac{7}{8}$
Option 2: $\frac{11}{15}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{2}{3}$
Correct Answer: $\frac{7}{8}$
Solution : Given numbers are = $\frac{2}{3},\frac{5}{6},\frac{11}{15},\frac{7}{8}$ LCM of denominators (3, 6, 15, 8) = ${3×2×5×4} = 120$ Making all denominators the same for comparison, $⇒ \frac{2}{3}\times \frac{40}{40} = \frac{80}{120} $ $⇒ \frac{5}{6}\times \frac{20}{20} = \frac{100}{120} $ $⇒ \frac{11}{15}\times \frac{8}{8} = \frac{88}{120} $ $⇒ \frac{7}{8}\times \frac{15}{15} =\frac{105}{120} $ Now, compare the numerators (105 > 100 > 88 > 80) So, $\frac{7}{8}$ is the greatest fraction. Hence, the correct answer is $\frac{7}{8}$.
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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 : 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 : $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=?$
Option 1: 5
Option 2: 4
Option 3: 3
Option 4: 2
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 : The greatest among the following numbers $(3)^{\frac{1}{3}}, (2)^{\frac{1}{2}}, 1, (6)^{\frac{1}{6}}$ is:
Option 1: $(2)^{\frac{1}{2}}$
Option 2: 1
Option 3: $(6)^{\frac{1}{6}}$
Option 4: $(3)^{\frac{1}{3}}$
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