CTET Paper II (Mathematics and Science) Nov 2012 Solved Paper

Concept:Compare fractions by converting them to a common denominator to see which lies between two given values.Explanation:The fractions are $\frac{3}{8}, \frac{4}{5}, \frac{31}{40}, \frac{9}{20}, \frac{7}{10}$.The required range is between $\frac{1}{2}$ and $\frac{3}{4}$.Find the LCM of all denominators: 8, 5, 40, 20, 10, 2, 4. The LCM is 40.Convert each fraction to denominator 40:$\frac{3}{8} = \frac{15}{40}$, $\frac{4}{5} = \frac{32}{40}$, $\frac{31}{40} = \frac{31}{40}$, $\frac{9}{20} = \frac{18}{40}$, $\frac{7}{10} = \frac{28}{40}$.Convert the range boundaries to denominator 40: $\frac{1}{2} = \frac{20}{40}$ and $\frac{3}{4} = \frac{30}{40}$.Only $\frac{28}{40}$ lies between $\frac{20}{40}$ and $\frac{30}{40}$.Thus, $\frac{28}{40} = \frac{7}{10}$ is the fraction that is greater than $\frac{1}{2}$ and less than $\frac{3}{4}$.Answer:D. $\frac{7}{10}$