Question

__________ are rational numbers between between 5 and -2.

• A. $5,\frac{33}{4},\frac{3}{2},-\frac{1}{4},-2$
• B. $\frac{13}{4},\frac{3}{2},-\frac{1}{4}$
• C. $5,\frac{13}{4},\frac{13}{2},-\frac{1}{4},-2$
• D. none of the above

Answer 1

The correct option is B $\frac{13}{4},\frac{3}{2},-\frac{1}{4}$

A rational number between two numbers $a$ and $b=\frac{(a+b)}{2}$
So, a rational number between $5$ and $-2=\frac{(5-2)}{2}=\frac{3}{2}$

Now, another rational number between $5$ and $\frac{3}{2}=\frac{(5+\frac{3}{2})}{2}=\frac{13}{4}$

Another rational number between $\frac{3}{2}$ and $-2=\frac{\left(\frac{3}{2}\right)-2}{2}=-\frac{1}{4}$
$\therefore \frac{13}{4},\frac{3}{2},-\frac{1}{4}$ are the rational numbers between $5$ and $-2$