Question

find three rational number between

Answer 1

I hope it helps u. . . . .

Answer 2

Answer:

$\text{a. The number are m = }\frac{-2}{5}\text{ and n = }\frac{11}{10}$

Let the rational number which are to be inserted = p, q and r

Now, both the numbers are rational and to insert a rational number, p between a rational number we can use the relation :

$p = \frac{1}{2}\times (m +n)\\\\\implies p=\frac{1}{2}\times (\frac{-2}{5} + \frac{1}{2})\\\\\implies p= \frac{1}{2}\times \frac{1}{10} \\\\\implies p = \frac{1}{20}\\\\\text{Now, similarly inserting the other two rational numbers} \\\\\implies q=\frac{1}{2}\times (\frac{-2}{5} + \frac{1}{20})\\\\\implies q= \frac{1}{2}\times \frac{-9}{20} \\\\\implies q = \frac{-9}{40}\\\\\implies Similarly, r=\frac{1}{2}\times (\frac{-2}{5} + \frac{-9}{40})\\\\\implies r= \frac{1}{2}\times \frac{-5}{8} \\\\\implies r = \frac{-5}{16}$

$\text{b. The number are m = }\frac{1}{2}\text{ and n = }\frac{1}{3}$

Let the rational number which are to be inserted = p, q and r

Now, both the numbers are rational and to insert a rational number, p between a rational number we can use the relation :

$p = \frac{1}{2}\times (m +n)\\\\\implies p=\frac{1}{2}\times (\frac{1}{2} + \frac{1}{3})\\\\\implies p= \frac{1}{2}\times \frac{5}{6} \\\\\implies p = \frac{5}{12}\\\\\text{Now, similarly inserting the other two rational numbers} \\\\\implies q=\frac{1}{2}\times (\frac{1}{2} + \frac{5}{12})\\\\\implies q= \frac{1}{2}\times \frac{11}{12} \\\\\implies q = \frac{11}{24}\\\\\implies Similarly, r=\frac{1}{2}\times (\frac{1}{2} + \frac{11}{24})\\\\\implies r= \frac{1}{2}\times \frac{23}{24} \\\\\implies r = \frac{23}{48}$