Question

insert two rational number between 1/2 and 1/3

Answer 1

✪ 1/2 = 1/2*3/3

 

           = 3/6*6/6

  

           = 18/36

✪ 1/3 = 1/3 *2/2

   

           = 2/6*6/6

 

           = 12/36

∴ 5 Rational numbers between ½ and 1/3 are:

✪ 13/36

✪ 14/36

✪ 15/36

✪ 16/36

✪ 17/36.

Answer 2

Answer:

Three Rational Number between given rational number are 22/60 , 25/60 and  28/60.

Step-by-step explanation:

We are given with two rational numbers. = $\frac{1}{3}\:\:and\:\:\frac{1}{2}$

We need to find three rational between given rational numbers.

First we convert them in like rational numbers means rational numbers with same denominators.

LCM of 2 and 3 = 6

So,

$\frac{1}{3}=\frac{1\times2}{3\times2}=\frac{2}{6}$

$\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}$

Now clearly from like numbers their are no rational number between them.

Now we increase the vale of there numerator such that we get required number of rational between obtained rational numbers.

Consider,

$\frac{2}{6}=\frac{2\times10}{6\times10}=\frac{20}{60}$

$\frac{3}{6}=\frac{3\times10}{6\times10}=\frac{30}{60}$

Rational number between given numbers are 22/60 , 25/60 and  28/60.

Therefore, Three Rational Number between given rational number are 22/60 , 25/60 and  28/60.