Question

find five rational numbers between 2 by 3 and 4 by 5

Answer 1

Hii..

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Here is ur answer :-

2/3 and 4/5

Multiply 2/3 by 5/5 and 4/5 by 3/3 to make the denominator equal.

2/3 * 5/5 and 4/5*3/3

= 10/15 and 12*15

Again multiply both by 5/5

10/15 * 5/5 and 12/15 * 5/5

50/ 75 and 60/75

So, rational number between 50/75 and 60/75 are :-

51/75 , 52/75 , 53/75 , 54/75 , 55*75 , 56/75 , 57/75 , 58/75 , 58/75 , 59/75

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Hope it helps!! ✌✌

Answer 2

Heya !!!

This is Your Answer...

Given :
2/3 and 4/5.

I have a formula to solve it, and it's very to get infinite rational numbers between two rational numbers.

Formula is :
$a + \frac{n(b - a)}{n + 1}$
where,
a and b are two rational numbers and n = 1, 2, 3, ....., n.

Now, Putting values....
$= \frac{2}{3} + \frac{1( \frac{4 }{5} - \frac{2}{3} )}{1 + 1} \\ = \frac{2}{3} + \frac{( \frac{12}{15} - \frac{10}{15} )}{2} \\ = \frac{2}{3} + \frac{2}{15} \times \frac{1}{2} \\ = \frac{10}{15} + \frac{1}{15} = \frac{11}{15}$
Therefore, First number is 11/15.

Now, Second =
$= \frac{2}{3} + \frac{2( \frac{4 }{5} - \frac{2}{3} )}{1 + 2} \\ = \frac{2}{3} + \frac{2( \frac{12}{15} - \frac{10}{15} )}{3} \\ = \frac{2}{3} + \frac{4}{15} \times \frac{1}{3} \\ = \frac{30}{45} + \frac{4}{45} = \frac{34}{45}$
Now, third =
$= \frac{2}{3} + \frac{3( \frac{4 }{5} - \frac{2}{3} )}{3 + 1} \\ = \frac{2}{3} + \frac{3( \frac{12}{15} - \frac{10}{15} )}{4} \\ = \frac{2}{3} + \frac{6}{15} \times \frac{1}{4} \\ = \frac{20}{30} + \frac{3}{30} = \frac{23}{30}$

Use n = 4, 5, 6, ..... to obtain more.

Hope It Helps