Question

Given the following rational numbers, choose the ones that lie between 1 and 3.

• A. $\frac{3}{2}$
• B. $\frac{4}{2}$
• C. $\frac{7}{2}$
• D. $\frac{11}{2}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{3}{2}$
B $\frac{4}{2}$

We know that 1 = $\frac{2}{2}$

and 3 = $\frac{3\times 2}{1\times 2}=\frac{6}{2}$

Consider $\frac{2}{2}$, $\frac{3}{2}$, $\frac{4}{2}$, $\frac{7}{2}$, $\frac{11}{2}$ and $\frac{6}{2}$.

Since denominators are same, on comparing the numerators we get

$\frac{2}{2}$ < $\frac{3}{2}$ < $\frac{4}{2}$ < $\frac{6}{2}$ < $\frac{7}{2}$ < $\frac{11}{2}$

$\Rightarrow$ $1$ < $\frac{3}{2}$ < $\frac{4}{2}$ < $3$ < $\frac{7}{2}$ < $\frac{11}{2}$

Therefore, rational numbers $\frac{3}{2}$ and $\frac{4}{2}$ lie between 1 and 3.