Question

find a rational number line between 7/10 and 10/17.​

Answer 1

Steps to find rational no. between a and b, where a and b are rational no.s

- Represent a and b in terms of common denominator

- To get same denominator in both of a and b,

Find the LCM of the denominator.

- Multiply and divide each of them so that the denominator becomes Same in all of them. (i.e., LCM)

- #### In the rational no.s with same denominator, the one which has smallest numerator value is the smallest rational no..

i.e., In two rational numbers p/D and q/D ; where p<q

the number r/D is the number between p/D and q/D ; where p<r<q viz., r lies in between

Now,

7/10 ; 10/17

Here, We have 10 and 17 in the denominators of both numbers.

LCM = 170

7/10 = 7/10 × 17/17 = (17 × 7)/170 = 119/170

10/17 = 10/17 × 10/10 = (10×10)/170 = 100/170

Here, we now got the numbers in term of same denominator.

Here, the smallest rational no. is 100/170

and largest rational no. is 119/170

Now, you can take any No. b/w 100 and 119 as required Numerator and 170 as Denominator.

Say 125.

•°• Required No. = 125/170 = 25/34

Note : This is just one of rational no. that lies in between 7/10 and 10/17; there are many possibilities.