Question

find six rational numbers between -1 and 0​

Answer 1

A simple way to find out rational number between two numbers a and b is by simple using the formula: $\frac {a + b}{2}$.

So, 1st rational number between -1 and 0 can be $\frac{-1+0}{2}$ i.e. $\frac{-1}{2}$.

Now, finding another rational number between 0 and $\frac{-1}{2}$ :

$\Rightarrow \frac{\frac{-1}{2} +0}{2}}\\\Rightarrow \frac{-1}{4}$

Similarly, finding rational number between -1 and $\frac{-1}{2}$:

$\Rightarrow \frac{-1+\frac{-1}{2}}{2}\\\Rightarrow \frac{-3}{4}$

Finding rational number between $\frac{-1}{2}$ and $\frac{-1}{4}$ :

$\Rightarrow \frac{\frac{-1}{4}+\frac{-1}{2}}{2}\\\Rightarrow \frac{-3}{8}$

Finding rational number between $\frac{-1}{2}$ and $\frac{-3}{4}$ :

$\Rightarrow \frac{\frac{-3}{4}+\frac{-1}{2}}{2}\\\Rightarrow \frac{-5}{8}$

Finding rational number between $0$ and $\frac{-1}{4}$ :

$\Rightarrow \frac{\frac{-1}{4}+0}{2}\\\Rightarrow \frac{-1}{8}$

So, the required rational numbers are as follows:

$\{\frac{-3}{4},\frac{-5}{8},\frac{-1}{2},\frac{-3}{8},\frac{-1}{4},\frac{-1}{8}\}$

Answer 2

Answer:

Answer in the attachment...