Question

Find any five rational numbers between 1/2 and 2/3​

Answer 1

Let x = 1/2 and y = 2/3. clearly, x < y. n= 6

Let d = y-x / (n+1) = 2/3-1/2/6+1 = 1/6×1/7 = 1/42

so the five rational number between 1/2 and 2/3

(x+d) = (1/2 + 1/42) = 22/42

(x+2d) = (1/2+ 2× 1/42) = 23/42

(x+3d) = ( 1/2 + 3×1/42) = 24/42

(x+4d) = (1/2 + 4×1/42) = 25/42

(x+5d) = (1/2 + 5×1/42) = 26/42

Five rational numbers are , 22/42 ,23/42 ,24/42 ,25/42 ,26/42.

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