CTET Paper II (Mathematics and Science) 20 Dec 2021 Solved Paper

Concept:A rational number is any number that can be written as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. To find a rational number between two given fractions, compare their decimal values or convert them to equivalent fractions with a common denominator.Explanation:First, convert the given fractions to decimals:$-\frac{5}{6} \approx -0.833$ and $\frac{3}{8} = 0.375$.Now, check each option to see which decimal lies between $-0.833$ and $0.375$:Option A: $-\frac{7}{8} = -0.875$ (too low)Option B: $-\frac{8}{9} \approx -0.889$ (too low)Option C: $\frac{1}{3} \approx 0.333$ (lies between $-0.833$ and $0.375$)Option D: $\frac{5}{6} \approx 0.833$ (too high)Alternatively, use the LCM method. LCM of 6 and 8 is 24. Write both fractions with denominator 24:$-\frac{5}{6} = -\frac{20}{24}$ and $\frac{3}{8} = \frac{9}{24}$.Any fraction between $-\frac{20}{24}$ and $\frac{9}{24}$ is a valid rational number. Among the options, $\frac{1}{3} = \frac{8}{24}$ lies between $-\frac{20}{24}$ and $\frac{9}{24}$.Answer:C. $\frac{1}{3}$