Question

Find four rational numbers between -3/2 and 5/3

Answer 1

Answer:

Four rational numbers between $-\frac{3}{2}$ and $\frac{5}{3}$ are $x_{1} = -\frac{13}{15}$, $x_{2} = -\frac{7}{30}$, $x_{3} = \frac{2}{5}$ and $x_{4} = \frac{31}{30}$.

Step-by-step explanation:

First, we calculate the distance between $-\frac{3}{2}$ and $\frac{5}{3}$:

$r = \frac{5}{3}-\left(-\frac{3}{2}\right)$

$r = \frac{5}{3}+\frac{3}{2}$

$r = \frac{10+9}{6}$

$r = \frac{19}{6}$

Then, we find four rational numbers by using the following formula:

$x = -\frac{3}{2}+\left(\frac{n}{5})\cdot \left(\frac{19}{6} \right)$

First number ($n = 1$)

$x_{1} = -\frac{13}{15}$

Second number ($n = 2$)

$x_{2} = -\frac{7}{30}$

Third number ($n = 3$)

$x_{3} = \frac{2}{5}$

Fourth number ($n = 4$)

$x_{4} = \frac{31}{30}$