Math, asked by PrimeDevansh, 10 months ago

6. Find ten rational numbers between 2/3 and 2/5​

Answers

Answered by sarthakbts
2

Answer:

Hello , .........

here is Ur answer ★

we have to find ten rational number between

\frac{2}{3} + \frac{2}{5}

3

2

+

5

2

Sol.

Five rational number 2/3 and 2/5 .

Let

\begin{lgathered}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}\end{lgathered}

x=

3

2

y=

5

2

andn=10

d= (

n+1

y−x

)=>

10+1

5

2

3

2

=>

11

15

4

=>

15

4

×

11

1

=

165

4

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)

=>

\begin{lgathered}( \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} )\end{lgathered}

(

3

2

+

165

4

),(

3

2

+

165

8

),(

3

2

+

165

12

),(

3

2

+

165

16

),

(

3

2

+

165

20

),(

3

2

+

165

24

),(

3

2

+

165

28

),(

3

2

+

165

32

),

(

3

2

+

165

36

),(

3

2

+

165

40

)

if we do Lcm all these ......

we get ★

\begin{lgathered}\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}\end{lgathered}

165

114

,

165

118

,

165

122

,

165

126

,

165

130

,

165

134

,

165

138

,

165

142

,

165

146

,

165

150

HERE is ten rational numbers between 2/3 and 2/5.

hope it's helpful for you☺☺

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