Question

S) Find 2 rational numbers between these two fractions 1413/5689 1838/7370

Answer 1

Take the average, which always lies in the middle of any two numbers:

(1413/5689 + 1838/7370) / 2 = 5217548/20963965

To get another number, take the average of this number with any of the first two. For example,

(1413/5689 + 5217548/20963965)/2 = 10424453/41927930

Notice that

1413/5689 ≈ 0.248374

10424453/41927930 ≈ 0.248628 … … … (the second average, between the first number and the first average)

5217548/20963965 ≈ 0.248882 … … … (the first average of the given two numbers)

1838/7370 ≈ 0.249389

(underlined for emphasis)