Question

insert 5 ratinal no. between
$\frac{1}{2}$
$\frac{2}{3}$

Answer 1

Your question needs a correction :


Correct question : Insert 5 "rational" no. between ½ and ⅔




Solution : —


Given two rational numbers : ½ and ⅔



in both the fraction denominator is different, to make them equal taking LCM of both the different denominators.


LCM of 2 and 3 = 6




Now, $\dfrac{1}{2}=\dfrac{1}{2}\times\dfrac{3}{3}=\dfrac{3}{6}$


And, $\dfrac{2}{3}=\dfrac{2}{3}\times\dfrac{2}{2}=\dfrac{4}{6}$




Now, we have to find rational numbers between $\dfrac{3}{6} \: \: and \: \: \dfrac{4}{6}$


$\dfrac{3}{6} > \dfrac{4}{6}$




As we have to find 5 numbers, multiply by ( 5 + 1 ) i.e. 4 on denominator and numerator both.



$\dfrac{3}{6} \times \dfrac{6}{6} > \dfrac{4}{6} \times \dfrac{6}{6} \\ \\ \\ \\ \dfrac{18}{36} > \dfrac{24}{36}$



Now, denominator is same. numbers between 12 and 16 = 18>19>20>21>22>23>24




Now, numbers between ½ and ⅔ are : —

$\frac{19}{36} \\ \\ \frac{20}{36} \\ \\ \frac{21}{36} \\ \\ \frac{22}{36} \\ \\ \frac{23}{36}$



They can be reduced to their lowest ( simplified ) term.

Answer 2

rational numbers between $\frac{1}{2}$ , $\frac{2}{3}$

by equalling they denominator by calculating LCM .

= $\frac{3}{6}$ , $\frac{4}{6}$

= $\frac{3}{6} × \frac{10}{10} , \frac{4}{6} × \frac{10}{10}$

= $\frac{30}{60}$ , $\frac{40}{60}$

5 rational numbers between $\frac{1}{2} , \frac{2}{3}$ = $\frac{31}{60} , \frac{32}{60} , \frac{33}{60} , \frac{34}{60} , \frac{35}{60}$