Find a rational number between 5 7 and 9 11 .

Given to find a rational number between 5 7 and 9 11 . Now, we make the denominators of the numbers equal. 5 7 = 5 × 11 7 × 11 = 55 77 And 9 11 = 9 × 7 11 × 7 = 63 77 Thus, a rational number between the given numbers is 56 77 . Therefore, a rational number between 5 7 and 9 11 is 56 77

Find an irrational number between 5 7 and 9 11 .

Given to find an irrational number between 5 7 and 9 11 . Now, 5 7 = 0 . 714285714285 . . . . . . . . . . = 0 . 714285 And 9 11 = 0 . 8181 . . . . = 0 . 81 The number formed by the next two digits of the decimal point of the first number is 71 and that of the second number is 81 . So, constructing an irrational number by taking any one value between 71 and 81 , we get 720720072000 . . . . . . . . . Thus, an irrational number between 0 . 714285 and 0 . 81 is 0 . 720720072000 . . . . . . . . . . Therefore, an irrational number between 5 7 and 9 11 is 0 . 720720072000 . . . . . . . . . .

What should be subtracted from the number e + 1 e - 1 to get a rational number?

Given, e + 1 e - 1 = e 2 - 1 2 = e - 1 If we add - e with e - 1 , then we get, - e + e - 1 = - 1 Here, - 1 is a rational number. Therefore, we must add - e with e + 1 e - 1 to get a rational number.