Question

Find ten rational numbers between 2/3 and 2/5

Answer 1

Hello , .........
here is Ur answer ★

we have to find ten rational number between
$\frac{2}{3} + \frac{2}{5}$

Sol.

Five rational number 2/3 and 2/5 .

Let
$x = \frac{2}{3} \: \: y = \frac{2}{5} \: \: and \: \: n = 10 \\ \\ d = \ ( \frac{y - x}{n + 1} ) = > \frac{ \frac{2}{5} - \frac{2}{3} }{10 + 1} = > \frac{ \frac{4}{15} }{11} \\ \\ = > \frac{4}{15} \times \frac{1}{11} = \frac{4}{165}$

Five rational number between X and Y are :

=> (x+d), (x+2d) , (x+3d) , (x+4d) , (x+5d) , (x+6d) , (x+7d) , (x+8d) , (x+9d) , (x+10d)

=>
$( \frac{2}{3} + \frac{4}{165} ), \: \: ( \frac{2}{3} + \frac{8}{165} ), \: \: ( \frac{2}{3} + \frac{12}{165} ) ,\: \: ( \frac{2}{3} + \frac{16}{165} ), \\ \\ ( \frac{2}{3} + \frac{20}{165} ), \: \: ( \frac{2}{3} + \frac{24}{165} ) ,\: \: ( \frac{2}{3} + \frac{28}{165} ) ,\: \: ( \frac{2}{3} + \frac{32}{165}), \: \: \\ \\ ( \frac{2}{3} + \frac{36}{165} ) ,\: \: ( \frac{2}{3} + \frac{40}{165} )$

if we do Lcm all these ......
we get ★

$\frac{114}{165} ,\: \: \frac{118}{165}, \: \: \frac{122}{165}, \: \: \frac{126}{165} ,\: \: \frac{130}{165} ,\: \: \frac{134}{165} ,\: \: \frac{138}{165} ,\\ \\ \frac{142}{165} ,\: \: \frac{146}{165} ,\: \: \frac{150}{165}$
HERE is ten rational numbers between 2/3 and 2/5.
hope it's helpful for you☺☺

Answer 2

Answer:

$\frac{62}{150},\frac{63}{150},\frac{64}{150},\frac{65}{150},\frac{66}{150},\frac{67}{150},\frac{68}{150},\frac{69}{150},\frac{70}{150},\frac{71}{150}$                              

Step-by-step explanation:

Given : Numbers $\frac{2}{3}$ and $\frac{2}{5}$

To find : Find ten rational numbers between numbers?

Solution :

Rational number is defined as the number which can be written in p/q form where p and q are integers and q is nonzero or written in fraction form.

$a=\frac{2}{3}$

$a=\frac{2\times 50}{3\times 50}$

$a=\frac{100}{150}$

$b=\frac{2}{5}$

$b=\frac{2\times 30}{5\times30}$

$b=\frac{60}{150}$

Now, The number between 100 and 60 are 62,63,64,65,66,67,68,69,70,71.

The rational number between $\frac{2}{3}$ and $\frac{2}{5}$ are

$\frac{62}{150},\frac{63}{150},\frac{64}{150},\frac{65}{150},\frac{66}{150},\frac{67}{150},\frac{68}{150},\frac{69}{150},\frac{70}{150},\frac{71}{150}$