Question

insert 5 rational number between1/3 and5/9

Answer 1

1×9/3×9=9/27

5×3/9×3=15/27
so,the 5 rational numbers are-
10/27, 11/27, 12/27, 13/27, 14/27

may its help you .........

Answer 2

Hello Mate!

To find an rational number between 1/3 and 5/9,
we will use

$\frac{r + s}{2} formula \\ (\frac{1}{3} + \frac{5}{9} ) \div 2 \\ \frac{8}{9} \times \frac{1}{2} = \frac{8}{18}$

In 1/3 and 8/18 we have,

$( \frac{1}{3} + \frac{1}{18} ) \div 2 \\ \frac{7}{18} \times \frac{1}{2} = \frac{7}{36}$

In 1/3 and 7/36 we have,

$( \frac{1}{3} + \frac{7}{36} ) \div 2 \\ \frac{19}{36} \times \frac{1}{2} = \frac{19}{72}$

Now, in 8/18 and 5/9 we have,

$(\frac{8}{18} + \frac{5}{9} ) \div 2 \\ \frac{18}{18} \times \frac{1}{2} = \frac{18}{36}$

In 18/36 and 5/9 we have ,

$(\frac{18}{36} + \frac{5}{9} ) \div 2 \\ \frac{38}{36} \times \frac{1}{2} = \frac{38}{72}$

So, finally we get : 1/3 < 19/72 < 7/36 < 8/18 < 18/ 36 < 38/ 72 < 5/9

Hope it helps☺!✌