Question

Which of the rational number lies between $-\frac{2}{3}$ and $\frac{1}{4}$

• A. $\frac{-5}{24}$
• B. $\frac{25}{12}$
• C. $\frac{51}{24}$
• D. $\frac{5}{12}$

Answer 1

The correct option is A $\left(\frac{-5}{24}\right)$

Given fractions $-\frac{2}{3}$ and $\frac{1}{4}$
Since, the denominators are not equal, so lets make denominators are equal.
Case (i): Multiplying $\frac{4}{4}$ with $-\frac{2}{3}$ and $\frac{3}{3}$ with $\frac{1}{4}$
Thus,$\frac{4}{4}\times -\frac{2}{3}=-\frac{8}{12}$ and $\frac{3}{3}\times \frac{1}{4}=\frac{3}{12}$
By observing the given four options we say that, none of the option value lies between $-\frac{8}{12}$ and $\frac{3}{12}$.
Similar way,
Case(ii): Multiplying $\frac{8}{8}$ with $-\frac{2}{3}$ and $\frac{6}{6}$ with $\frac{1}{4}$
Thus, $\frac{8}{8}\times -\frac{2}{3}=-\frac{16}{24}$ and $\frac{6}{6}\times \frac{1}{4}=\frac{6}{24}$
By observing the given four options we say that, the option (A) value $\frac{-5}{24}$ lies between $-\frac{16}{24}$ and $\frac{6}{24}$
Hence, it is clear that $-\frac{5}{24}$ lies between the given fractions.