Question

Find three rational numbers between

$-2$ and $5$.

Answer 1

Step 1: Finding the value of $d$

Here, $x=-2$ and $y=5$ are two rational numbers such that $x<y$.

Then $3$ rational numbers lying between $x$ and $y$ are $(x+d),(x+2d)$ and $(x+3d)$ where $d=\frac{y-x}{n+1}$ is the equal distance between the rational numbers and $n$is the number of terms to be found.

Substitute the given values to attain the value of $d$.

$$\begin{gathered} d=\frac{y-x}{n+1} \\ =\frac{5-(-2)}{3+1} \\ =\frac{5+2}{4} \\ =\frac{7}{4} \end{gathered}$$

Step 2: Finding the rational numbers.

The three rational numbers can be calculated by substituting the values of $x$ and $d$ in $(x+d),(x+2d)$ and $(x+3d)$.

So, the numbers are

$(-2+\frac{7}{4}),(-2+\frac{14}{4})$ and $(-2+\frac{21}{4})$ which can be simplified as

$-\frac{1}{4},\frac{3}{2}$ and $\frac{13}{4}$.

Hence, the required three rational numbers between $-2$ and $5$ are $-\frac{1}{4},\frac{3}{2}$ and $\frac{13}{4}$.