Question

Find three rational numbers between $\dfrac{{ - 3}}{{14}}$ and $\dfrac{6}{{14}}$.

Answer 1

Hint: In order to solve this question obtain fractional numbers between them by doing the $\dfrac{{{\text{a + b}}}}{{\text{c}}}$ where c is greater than one.

Complete step-by-step solution:
As we know rational numbers are those which can be expressed in the form $\dfrac{p}{q}$.
Where q is not equals to zero.
Therefore the rational number between two numbers say a and b can be obtained by doing the operation $\dfrac{{{\text{a + b}}}}{2}$.
The rational number between $\dfrac{{ - 3}}{{14}}$ and $\dfrac{6}{{14}}$ is
$\dfrac{{\dfrac{{ - 3}}{{14}} + \dfrac{6}{{14}}}}{2} = \dfrac{3}{{28}}$
The rational number between $\dfrac{3}{{28}}$ and $\dfrac{6}{{14}}$ is
$\dfrac{{\dfrac{3}{{28}} + \dfrac{6}{{14}}}}{2} = \dfrac{{15}}{{56}}$
Therefore the rational number between $\dfrac{{15}}{{56}}$ and $\dfrac{6}{{14}}$ is
$\dfrac{{\dfrac{{15}}{{56}} + \dfrac{6}{{14}}}}{2} = \dfrac{{39}}{{112}}$
Therefore the 3 rational numbers between $\dfrac{{ - 3}}{{14}}$ & $\dfrac{6}{{14}}$ are
$\dfrac{3}{{28}},\,\dfrac{{15}}{{56}},\,\dfrac{{39}}{{112}}$.

Note: In mathematics, a rational number is a number that can be expressed as the quotient or fraction $\dfrac{p}{q}$ of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.