Question

Which of the pairs of rational no. lie between 2/3 and 4/5??

Answer 1

heya !!!!

2/3 = 2 x 5 / 3  x 5 

       = 10 / 15 

4/5 = 4 x 3 / 5 x 3 

       12 / 15 

we can find 5 rational numbers betwen 2/3 and 4/5 by multiplying them with 5 + 1 = 6 

10 / 15  X 6 /6 

= 60 / 90 

12/ 15 X 6 /6 

= 72 / 90 

the rational numbers = 61 / 90  62 /90  63 /90  64/90  65/90  66/90   67 /90 .....

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Answer 2

Hello ,

Infinite numbers lie between any two rational numbers a and b
As,
To find them first of all we will make their denominators same
2/3 × 5/5 = 10/15
4/5 × 5/5 = 12/15

11/15 is between them.

Note to find suppose 9 numbers between them multiply 9+1 = 10 to both numerator and denominator .
We know that numbers that lie between 11/15 and 10/15 also lie between 12/15 and 10/15
So,
$\frac{10 \times 10}{15 \times 10}$

= 100/ 150

$\frac{11 \times 10}{150}$
= 110/150

Now write ak the numbers between 110 and 100 taking denominator 150 to get 9 numbers between 2/3 and 4/5.

Hope this helps you ......
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